WISKUNDIGE GELETTERDHEID
GRAAD 11
NOG OEFENINGE
  
Koers, verhouding en eweredigheid : antwoorde.
  
MATHEMATICAL LITERACY
GRADE 11
MORE EXERCISES
  
Rate, ratio and proportion : answers.
  
 Antwoorde 1 / Answers 1 
  
  
        Hier is die reëls vir deelbaarheid 'n wins.
  
        Die reëls : 'n Getal is deelbaar deur
          2 :  as die getal op 'n 0, 2, 4, 6 of 8 eindig.
          3 :  tel die sysfers waaruit die getal
                bestaan op.
                As die som uit meer as 1 syfer
                bestaan, tel die syfers weer op,
                totdat 'n een-syfer getal gekry word.
                Hierdie 1 syfer som word die
                digitale wortel van die oorspronklike
                getal, p, genoem. As die digital wortel
                'n veelvoud van 3 is, is die oorspronklike
                getal, p, deelbaar deur 3.
          4 :  as die laaste twee syfers van die getal
                deelbaar is deur 4.
          5 :  as die getal op 'n 0 of 5 eindig.
  
          6 :  as die getal deur beide
                2 en 3 deelbaar is.
          7 :  Daar is geen maklike reël nie.
          8 :  as die laaste drie syfers waaruit die
                getal bestaan, deelbaar is deur 8.
          9 :  as die digitale wortel gelyk is aan 9.
        10 :  as die getal op 'n 0 eindig.
        11 : Tel die syfers in die onewe posisies op.
               Doen dit ook met die syfers in die
               ewe posisies. As hierdie twee somme
               gelyk is, as die getal deelbaar deur 11,
               bv 29189160 is deelbaar deur 11 omdat
               2+1+9+6=18 (som van syfers in die
               onewe posisies) en 9+8+1+0=18 (som
               van syfers in die ewe posisies) en die
               twee somme is gelyk.
        12 :  as die getal deur beide 3 en 4 deelbaar is.
  
  
       Sommige sakrekenaars, bv. die
       Casio fx-82 ZA PLUS kan die priem faktore van
       'n getal bepaal. Dit is 'n groot bate. Bepaal
       die faktore van die teller en die noemer
       en kanselleer die gemene faktore.
  
  
    
        Here the rules for divisibility are a bonus.
  
        The rules : A number is divisible by
          2 :  if the number ends on a 0, 2, 4, 6 or 8.
          3 : add the digits that constituate the number.
               If the sum consists of more than 1 digit,
               add the digits again until a one digit
               number is obtained. This 1 digit number
               is called the digital root of the original
               number, p. If the digital root is a multiple
               of 3, then the original number, p, is
               divisible by 3.
  
  
          4 :  if the last two digits in the number
                is divisible by 4.
          5 :  if the last digit in the number is a
                0 or a 5.
          6 :  if the number is divisible by
                both 2 and 3.
          7 :  There is no eady rule.
          8 :  if the last three digits in the number
                is divisible by 8.
          9 :  if the digital root is equal to 9.
        10 :  if the last digit is a 0.
        11 :  Add the digits in the odd positions.
                Also add the digits in the even posiions.
                If these two sums are eual, the number
                is divisble by 11
                e.g. 29189160 is divisible by 11 because
                2+1+9+6=18 (sum of the digits in the odd
                positions) and 9+8+1+0=18 (sum of the
                digits in the even positions) and the
                two sums are equal.
        12 :  if the number is divisible by both 3 and 4.
  
  
       Some pocket calculators, like the
       Casio fx-82 ZA PLUS can calculate the prime
       factors of a number. This is also a huge bonus.
       Get the facors of the numerator and the
       denominator and cancel the common factors.
  
  
    
                38           2 × 19             2
        1.1  ───   =   ─────   =   ───
                57           3 × 19             3
  
                                                      [ 1.1 ]
  
    
                52           4 × 13             4
        1.3  ───   =   ─────   =   ───
                91           7 × 13             7
  
                                                      [ 1.3 ]
  
    
                247            13 × 19             13
        1.5  ────   =   ──────   =   ───
                437            19 × 23             23
  
                                                     [ 1.5 ]
  
  
      
                42            2 × 3 × 7              2
        1.2  ───   =   ───────   =   ───
               105           3 × 5 × 7              5
  
                                                            [ 1.2 ]
  
    
               136           8 × 17                8
        1.4  ───   =   ──────   =   ───
               221          13 × 17              13
  
                                                            [ 1.4 ]
  
    
                316          4 × 79               4
        1.6  ───   =   ──────   =   ───
                553          7 × 79               7
  
                                                            [ 1.6 ]
  
  
  
 Antwoorde 2 / Answers 2 
  
 Antwoorde 2.1 / Answers 2.1 
  
  
           7 albasters / marbles  Piet / Peter kry / gets  3   en / and  Jan / John  kry / gets  4
  
                           3         35                                         4         35
           Piet kry   ──  ×  ───    albasters  en Jan kry   ──  ×  ───    albasters
                           7          1                                          7          1
  
  
           Piet kry   15  albasters  en  Jan kry 20 albasters.
  
  
  
                                                                                                   3                                                   4
      Peter gets 3 marbles if there are (3 + 4) marbles, i.e. he gets ──   and John gets 4 marbles, i.e.  ──
                                                                                                   7                                                   7
  
  
                               3         35                                             4        35
           Peter gets   ──  ×  ───    marbles  and John gets   ──  ×  ───    marbles
                               7          1                                              7         1
  
  
           Peter gets   15  marbles  and  John gets 20 marbles.
  
  
  
  
                                                                        OF / OR    
  
         7 (3 + 4) albasters word verdeel in die verhouding 3 : 4
  
         Verdeel 35 albasters in dieselfde verhouding.
  
         Gestel Piet kry x albasters, dan kry Jan 35 ─ x
  
                                                                 Pieter           3             x
         Verdeel in dieselfde verhouding   :   ──────   =  ──   =  ─────
                                                                  Jan             4          35 ─ x
  
         Los op deur met KGV te vermenigvuldig   3 × (35 ─ x)  =  4 × x
  
                                                                            105 ─ 3x  =  4x
  
                                                                                    105  =  7x
  
                                                                                      15  =  x
  
          Piet kry  15  albasters  en  Jan kry  35 ─ 15  =  20  albasters
  
  
         7 (3 + 4) marbles are divided in the ratio 3 : 4
  
         Divide 35 marbles in the same ratio.
  
         Suppose Peter gets x marbles, then John gets  35 ─ x
  
                                                      Peter           3             x
         Divide in the same ratio   :   ──────   =  ──   =  ─────
                                                      John            4         35 ─ x
  
                                        Solve            3 × (35 ─ x)  =  4 × x
  
                                                                 105 ─ 3x  =  4x
  
                                                                         105  =  7x
  
                                                                           15  =  x
  
          Peter gets  15 marbles   and   John gets  35 ─ 15  =  20  marbles                               [ 2.1 ]
  
  
 Antwoorde / Answers 2.2 
  
  
          R 13 (4 + 9) :   A  kry / gets   R 4   en / and  B  kry / gets   R 9
  
                                                           4                                           9
          R 1               :   A kry / gets  R ──   en / and  B  kry  gets  R ───
                                                         13                                          13
  
  
                                                        4       1 378                                           9         1 378
          R 1 378       :  A kry / gets  R ── X ─────   en / and  B  kry  gets  R ─── X ─────
                                                       13          1                                             13            1
  
  
                                              d.i. / i.e  R 424                                       d.i. / i.e  R 954
  
                                  A kry / gets  R 424     en / and  B  kry  gets  R 954
  
  
                                                                              OF / OR    
  
                                                                                 4                                                       9
           A kry R4 as daar R(4 + 9) is, d.w.s hy kry   R ───      en B kry R9, d.w.s hy kry   R ───
                                                                                13                                                     13
  
  
                           3          1 378                           4           1 378
           A kry  R ───  ×  ─────      en B kry  R ───  ×  ─────    
                         13              1                             13              1
  
  
                               A kry  R 424     en   B  kry  R 954
  
  
                                                                                 4                                                        4
          A gets R 4 if there are R(4 + 9), i.e. he gets R ───     and B gets R 4, i.e. he gets  R ───
                                                                                13                                                       13
  
  
                            3          1 378                                4          1 378
           A gets  R ───  ×  ─────      and B gets  R ───  ×  ─────   
                           13             1                                  13            1
  
  
                                   A gets  R 424     and   B  gets  R 954                                              [ 2.2 ]
  
  
  
                                                                          OF / OR    
  
  
     R13 (4 + 9) word verdeel in die verhouding 4 : 9   /   R13 (4 + 9) is divided in the ratio 4 : 9
  
     Verdeel R1 378 in dieselfde verhouding.               /    Divide R1 378 in the same ratio.
  
     Gestel A kry Rx, dan sal B  R(1 378 ─ x)  kry.      / Suppose A gets Rx, then B will get  R(1 378 ─ x)
  
                                                                                                    A            R 4               R x
     Verdeel in dieselfde verhouding / Divide in the same ratio   :    ───   =  ────   =  ─────────
                                                                                                    B            R 9         R(1 378 ─ x)
  
     Los op deur met KGV te vermenigvuldig /  Solve by multiplying by the LCM
  
                                                                                                    4 × (1 378 ─ x)  =  9 × x
  
                                                                                                          5 512 ─ 4x  =  9x
  
                                                                                                                     512  =  13x
  
                                                                                                                     424  =  x
  
          A kry /nbsp;gets  R 424      en / and   B kry  /  John gets  R(1 378 ─ 424)  =  R 954
  
                                                                                                                                         [ 2.2 ]

  
  
 Antwoorde / Answers 2.3 
  
  
          R 14 (7 + 5 + 2) :   A  kry     R 7,   B  kry    R 5   en   C  kry    R 2
  
                                                       7                        5                              2
          R 1                   :   A kry   R ─── ,   B kry   R ───   en   C  kry   R ───
                                                      14                      14                            14
  
  
                                         7        18 214                    5        18 214                         2        18 214
      R 18 214   :  A kry  R ─── X ───── ,  B kry  R ─── X ─────  en  C  kry  R ─── X ──────
                                        14            1                      14           1                             14            1
  
  
                                  d.i.    R 9 107                    d.i.    R 6 505                       d.i.    R 2 602
  
  
                                   A kry    R 9 107 ,    B kry   R 6 505     en    C  kry   R 2 602
  
  
          R 14 (7 + 5 + 2) :   A  gets     R 7,   B  gets    R 5   en   C  gets    R 2
  
                                                         7                          5                                  2
          R 1                   :   A gets   R ─── ,   B gets   R ───   and   C  gets   R ───
                                                        14                        14                                14
  
  
                                            7       18 214                      5       18 214                             2        18 214
      R 18 214   :  A gets  R ─── X ───── ,  B gets  R ─── X ─────  and  C  gets  R ─── X ──────
                                          14           1                         14           1                                14           1
  
  
                                  d.i.    R 9 107                    d.i.    R 6 505                       d.i.    R 2 602
  
  
                                   A gets    R 9 107 ,    B  gets  R 6 505            and     C  kry  gets  R 2 602
  
                                                                                                                                         [ 2.3 ]
  
  
  
OF / OR 

  
                                                          7                                      5                                           2
    R(7 + 5 + 2) :   A kry R7 , d.w.s R ─── ,   B kry R5, d.w.s  R ───     en C kry R2, d.w.s  R ───
                                                        14                                     14                                         14
  
  
                           7         18 214                       5         18 214                             2         18 214
           A kry  R ───  ×  ─────       B kry  R ───  ×  ─────       en C kry  R ───  ×  ─────    
                         14             1                          14             1                                14              1
  
  
                        A kry  R 9 107                          B kry  R 6 505                  en   C  kry  R 2 602
  
  
                                                        7                                     5                                            2
    R(7 + 5 + 2) :   A gets R7 , i.e. R ─── ,   B gets R5, i.e.  R ───     and C gets R2, i.e.  R ───
                                                       14                                   14                                          14
  
  
                            7          18 214                         5         18 214                                2         18 214
           A gets  R ───  ×  ─────       B gets  R ───  ×  ─────       and C gets  R ───  ×  ─────    
                           14            1                             14             1                                   14             1
  
  
                    A gets  R 9 107                    B gets  R 6 505                  and   C  gets  R 2 602
  
                                                                                                                                        [ 2.3 ]
  
  
  
 Antwoorde / Answers 2.4 
  
  
          R 14 (3 + 11) :   C  kry / gets   R 3   en / and  D  kry / gets   R 11
  
                                                          3                                          11
          R 1               :   C kry / gets  R ──   en / and  D  kry  gets  R ──
                                                         14                                         14
  
  
                                                           3        323,64                                            11         323,64
          R 323,64       :  C kry / gets  R ─── X ──────   en / and  D  kry / gets  R ─── X ──────
                                                          14           1                                                 14            1
  
  
                                              d.i. / i.e  R 69,35                                        d.i. / i.e  R 254,29
  
                                  C kry / gets  R 69,35     en / and  D  kry  gets  R 254,29
  
                                                                                                                                          [ 2.4 ]
  
  
  
OF / OR 

  
                                                                                  3                                                     11
           C kry R3 as daar R(3 + 11) is, d.w.s hy kry  R ───    en D kry R11, d.w.s hy kry  R ───
                                                                                 14                                                    14
  
  
                          3        323,64                          4        323,64
           C kry  R ──  ×  ─────      en D kry  R ──  ×  ─────    
                         14            1                            14            1
  
  
                                  C kry  R 69,35     en   D  kry  R 254,29
  
  
                                                                                    3                                             11
          C gets R 3 if there are R(3 + 11), i.e. he gets R ───   and D gets R 11,   i.e.  R ───
                                                                                   14                                            14
  
  
                            3          323,64                              11         323,64
           C gets  R ───  ×  ─────      and D gets  R ───  ×  ──────
                           14             1                                  14              1
  
  
                                  C gets  R 69,35     en   D  kry  R 254,29                                            [ 2.4 ]
  
  
  
OF / OR 
  
           R14 (3 + 11) word verdeel in die verhouding 3 : 11
  
           Verdeel R323,64 in dieselfde verhouding.
  
           Gestel C kry Rx, dan sal D  R(323,64 ─ x)  kry.
  
                                                                     C            R 3                   R x
           Verdeel in dieselfde verhouding  :      ───   =  ────   =  ─────────
                                                                     D          R 11         R(323,64 ─ x)
  
           Los op deur met KGV te vermenigvuldig   :     3 X (323,64 ─ x)  =  11 X x
  
                                                                                      970,92 ─ 3x  =  11x
  
                                                                                              970,92  =  14x
  
                                                                                                69,35  =  x
  
          C kry  R 69,35     en   D  kry  R(323,64 ─ 69,35)  =  R 254,29                                     [ 2.4 ]
  
  
           R14 (3 + 11) is divided in the ratio 3 : 11
  
           Divide R323,64 in the same ratio.
  
           Suppose C gets Rx, then D will get  R(323,64 ─ x)
  
                                                        C            R 3                 R x
           Divide in the same ratio   :    ───   =  ────   =  ─────────
                                                        D           R 11         R(323,64 ─ x)
  
           Solve by multiplying by the LCM  :  3 × (323,64 ─ x)  =  11 × x
  
                                                                      970,92 ─ 3x  =  11x
  
                                                                              970,92  =  14x
  
                                                                                69,35  =  x
  
          C gets  R 69,35      and   D  gets  R(323,64 ─ 69,35)  =  R 254,29                              [ 2.4 ]
  
  
 Antwoorde / Answers 2.5 
  
  
           12 (5 + 7) osse / oxen  :   P  kry / gets   5   en / and  Q  kry / gets   7
  
                                                                           5                                           7
           1 os / ox                        :   P kry / gets   ───   en / and  Q  kry  gets   ───
                                                                          12                                         12
  
  
                                                                         5        96                                           7        96
           96 osse / oxen              :  P kry / gets   ─── X ───   en / and  Q  kry  gets   ─── X ───
                                                                        12         1                                         12         1
  
                                                             d.i. / i.e   40                                               d.i. / i.e   56
  
                                  P kry / gets  40 osse / oxen   en / and  Q  kry  gets  56  osse / oxen
  
  
OF / OR 
  
                                                                   5                                                   7
       (5 + 7) osse  :  P kry 5, d.w.s hy kry    ───      en Q kry 7, d.w.s hy kry    ───
                                                                  12                                                 12
  
  
                        5          96                           7          96
           P kry   ───  ×  ───      en Q kry   ───  ×  ───    
                       12           1                          12          1
  
  
                              P kry   40  osse   en   Q  kry   56 osse
  
  
                                                                    5                                                     7
       (5 + 7) oxen  :  P gets 5, i.e. he gets    ───      and Q gets 7, i.e. he gets    ───
                                                                   12                                                   12
  
  
                          5          96                              7          96
           P gets   ───  ×  ───      and Q gets   ───  ×  ───    
                         12           1                             12          1
  
  
                              P gets   40  oxen   and   Q  gets   56  oxen
  
  
  
OF / OR 
  
  
           12 osse (5 + 7) word verdeel in die verhouding 5 : 7
  
           Verdeel 96 osse in dieselfde verhouding.
  
           Gestel P kry x osse, dan sal Q  (96 ─ x)  osse  kry.
  
                                                                    P          5 osse             x  osse
           Verdeel in dieselfde verhouding  :    ───  =  ──────  =  ──────────
                                                                   Q          7 osse         (96 ─ x)  osse
  
           Los op deur met KGV te vermenigvuldig :    5 × (96 ─ x)  =  7 × x
  
                                                                                 480 ─ 5x  =  7x
  
                                                                                         480  =  12x
  
                                                                                            40 =  x
  
          P kry  40  osse    en   Q kry    (96 ─ 40)  =  56  osse                                                  [ 2.5 ]
  
  
           12 oxen (3 + 11) are divided in the ratio 5 : 7
  
           Divide 96 oxen in the same ratio.
  
           Suppose Q gets x oxen, then Q will get  (96 ─ x)  oxen
  
                                                        P           5 oxen                x  oxen
           Divide in the same ratio   :    ───   =  ──────   =  ──────────
                                                        Q           7 oxen          (96 ─ x)  oxen
  
           Solve by multiplying by the LCM   :   5 × (96 ─ x)  =  7 × x
  
                                                                      480 ─ 5x  =  7x
  
                                                                              480  =  12x
  
                                                                                40  =  x
  
          P  gets   40  oxen    and   Q  gets  (96 ─ 40)  =  56  oxen                                           [ 2.5 ]
  
  
 Antwoorde / Answers 2.6 
  
  
           13  =  (7 + 4 + 2)
  
           13 skape   :   R  kry  7,   S  kry    4   en   T  kry     2
  
                                              7                       4                            2
           1  skaap    :   R  kry   ─── ,   S  kry    ───   en    T  kry    ───
                                             13                     13                          13
  
  
                                          7         364                     4         364                       2        364
        364 skape  :  R  kry  ─── X ───── ,  S  kry  ─── X ────  en  T  kry  ─── X ────
                                         13          1                      13          1                       13          1
  
  
                                  d.i. / i.e   196                      d.i. / i.e   112                    d.i. / i.e   56
  
  
                   R kry  196  skape  ,    S kry   112  skape  en  T  kry  56  skape                          [ 2.6 ]
  
  
           13 sheep  :   R  gets  7,   S  gets  4   and  T  gets  2
  
                                              7                     4                           2
           1  sheep  :   R  gets  ─── ,  S  gets  ───  and  T  gets  ───
                                             13                   13                         13
  
  
                                         7         364                   4         364                           2         364
      364 sheep :  R  gets  ─── X ────   S  gets  ─── X ────  and  T  gets  ─── X ────
                                        13          1                    13           1                           13         1
  
  
                                d.i. / i.e   196                 d.i. / i.e   112                           d.i. / i.e   56
  
  
          R  gets  196  sheep ,    S  gets  112  sheep     and  T  gets  56  sheep                        [ 2.6 ]
  
  
  
OF / OR
  
  
                                                    7                                5                                   2
         13 skape :  R kry 7, d.w.s  ─── ,   S kry 4, d.w.s  ───   en T kry 2, d.w.s  ───
                                                   13                              13                                 13
  
  
                         7            364                      4            364                             2           364
           R kry   ───  ×  ─────       S kry   ───  ×  ─────       en T kry   ───  ×  ─────    
                        13            1                        13             1                             13             1
  
  
                  R kry   196  skape                 S kry  112  skape              en   T  kry  56  skape
  
                                                                                                                                         [ 2.6 ]
  
                                                   7                               4                                   2
         13 sheep :  R gets 7, i.e.  ─── ,   S gets 4, i.e.  ───   and T gets 2, i.e.  ───
                                                  13                             13                                 13
  
  
                           7          364                          4           364                                2            364
           R gets   ───  ×  ─────       S gets   ───  ×  ─────       and T gets   ───  ×  ─────    
                          13           1                           13            1                                 13             1
  
  
                  R gets  196  sheep                S gets  112  sheep            and   T  gets  56  sheep
  
                                                                                                                                         [ 2.6 ]
  
  
  
 Antwoorde / Answers 3 
  
  
            3.1  A : B : C  =  120 000  :  100 000  :  60 000
  
                   A : B : C  =  6  :  5  :  3      vereenvoudig deel met 20 000 / simplify divide by  20 000
  
                                                                                                                                          [ 3.1 ]
  
  
  
          3.2  R 14  =  R (6 + 5 + 3)
  
           R 14  :  A  kry  R 6,  B  kry  R 5  en  C  kry  R 3
  
                                      6                       5                           3
           R 1  :   A kry  R ─── ,   B kry  R ───  en  C  kry  R ───
                                     14                     14                          14
  
  
                                               6       48 601                    5        48 601                         3       48 601
           R 48 601   :  A kry  R ─── X ───── ,  B kry  R ─── X ─────  en  C  kry  R ─── X ─────
                                              14          1                       14            1                            14           1
  
  
                              d.i. / i.e  R 20 829                 d.i. / i.e  R 17 357,50           d.i. / i.e  R 10 414,50
  
  
              A kry  R 20 829 ,    B kry  R 17 357,50     en  C  kry  R 10 414,50                           [ 3.2 ]
  
  
  
  
           R 14  :  A  gets  R 6,  B  kry  R 5  and  C  gets  R 3
  
                                        6                         5                               3
           R 1  :   A gets  R ─── ,   B gets  R ───  and  C  gets  R ───
                                       14                       14                             14
  
  
                                                6        48 601                      5       48 601                             3        48 601
           R 48 601   :  A gets  R ─── X ───── ,  B gets  R ─── X ─────  and  C  gets  R ─── X ─────
                                               14           1                         14           1                                14           1
  
  
                                        i.e  R 20 829                        i.e  R 17 357,50                      i.e  R 10 414,50
  
  
                 A  gets  R 20 829 ,    B  gets  R 17 357,50    and  C  gets  R 10 414,50               [ 3.2 ]
  
  
  
  
  
OF / OR 
  
                                                    6                                         5                                           3
           R 14 :  A kry R6, d.w.s  R ─── ,     B kry R5, d.w.s  R ───     en C kry R3, d.w.s  R ───
                                                   14                                       14                                         14
  
  
                          6          48 601                       5          48 601                            3         48 601
           A kry  R ───  ×  ─────       B kry  R ───  ×  ─────       en C kry  R ───  ×  ─────    
                         14            1                           14             1                                14             1
  
  
                    A kry  R 20 829                  B kry  R 17 357,50                 en   C  kry  R 10 414,50
  
  
  
                                                   6                                       5                                             3
           R 14 :  A gets R6, i.e.  R ─── ,     B gets R5, i.e.  R ───     and C gets R3, i.e.   R ───
                                                  14                                     14                                           14
  
  
                             6          48 601                        5         48 601                                3         48 601
           A gets  R ───  ×  ─────       B gets  R ───  ×  ─────       and C gets  R ───  ×  ─────    
                           14             1                            14             1                                   14             1
  
  
                    A gets  R 20 829                  B gets  R 17 357,50            and   C  gets  R 10 414,50
  
  
                                                                                                                                        [ 3.2 ]
  
  
  
  
  
          3.3.1   A : B : C  =  120 000  :  100 000  :  60 000  +  5 000
  
                    A : B : C  =  120 000  :  100 000  :  65 000
  
                    A : B : C  =  24  :  20  :  13        vereenvoudig deel met 5 000  /   simplify divide by  5 000
  
                                                                                                                                     [ 3.3.1 ]
  
  
  
          3.3.2    R 57  =  R (24 + 20 + 13)
  
                    R 57  :   A  kry   R 24,   B  kry   R 20   en   C  kry   R 13
  
                                                24                       20                           13
                     R 1  :   A kry   R ─── ,   B kry   R ───   en   C  kry   R ───
                                                 57                      57                           57
  
  
                                            24     72 917,25                20     72 917,25                    13     72 917,25
            R72917,25 : A kry R ── X ─────── , B kry R ── X ─────── en C kry R ── X ───────
                                            57           1                       57           1                           57           1
  
  
                                    d.i.  R 30 702                       d.i.  R 25 585                   d.i.  R 16 630,25
  
  
                      A kry  R 30 702 ,    B kry  R 25 585      en  C  kry  R 16 630,25                   [ 3.3.2 ]
  
  
  
  
                    R 57  :   A  gets   R 24,   B  gets   R 20   and  C  gets   R 13
  
                                        24                        20                              13
             R 1  :  A gets  R ─── ,   B  gets  R ───   and  C  gets  R ───
                                        57                        57                              57
  
  
                                            24     72 917,25                  20     72 917,25                       13     72 917,25
          R72917,25 : A gets R ── X ─────── , B gets R ── X ─────── and C gets R ── X ───────
                                            57           1                         57           1                               57           1
  
  
                                         i.e  R 30 702                           i.e  R 25 585                    i.e  R 16 630,25
  
  
                           A  gets  R 30 702 ,    B  gets  R 25 585      and  C  gets  R 16 630,25
  
                                                                                                                                       [ 3.3.2 ]
  
  
  
  
  
 Antwoorde / Answers 4 
  
  
        4.1  Daar is 24 albasters
  
               As Jan 9 kry, dan kry
               Martiens (24 - 9) = 15
  
               Verhouding is :  
                           Jan : Martiens  =  9 : 15
                           Jan : Martiens  =  3 : 5
                                                             [ 4.1 ]
  
        4.2  R1 927 word verdeel
  
               As A R1 230 kry en B kry R574, dan
  
               sal C R(1 927 - 1 230 - 574) = R123 kry
  
               Verhouding is 
                A : B : C  =  1 230 : 574 : 123
  
              A : B : C  =  2X3X5X41 : 2X7X41 : 3X41
  
              A : B : C  =  30 : 14 : 3
                                                             [ 4.2 ]
  
  
  
        4.1  There are 24 marbles
  
                If John gets 9, then
                      Mike will get (24 - 9) = 15
  
               Ratio is :  
                      John : Mike  =  9 : 15
                      John : Mike  =  3 : 5
                                                        [ 4.1 ]
  
        4.2  R1 927 is divided
  
                 If A gets R1 230 and B gets R574, then
  
                 C will get R(1 927 - 1 230 - 574) = R123
  
               Ratio is 
                A : B : C  =  1 230 : 574 : 123
  
                A : B : C  =  2X3X5X41 : 2X7X41 : 3X41
  
                A : B : C  =  30 : 14 : 3
                                                           [ 4.2 ]
  
  
  
 Antwoorde / Answers 5 
  
  
        5.1  Vermeerdeer 82 kg in die verhouding 4 : 5
  
               4 kg moet nou 5 kg word.
  
                                         5
               1 kg moet nou ── kg word.
                                         4
  
                                          5          82
               82 kg moet nou ──  X  ───    kg word.
                                          4           1
  
                                 d.w.s.  102,5  kg
  
                Die vermeerderde massa is 102,5 kg
  
  
  
  
OF

               As die ou massa = 4 kg dan is
  
               die nuwe massa = 5 kg
  
               As die ou massa = 82 kg dan is
  
               die nuwe massa = x kg
  
                   ou massa             4          82
               ─────────  =  ───  =  ───
                nuwe massa           5           x
  
               Vereenvoudig  :  4 X x  =  5 X 82
  
                                                4x  =  410
  
                                                x  =  102,5
  
                Die vermeerderde massa
  
                is 102,5 kg.                       [ 5.1 ]
  
  
  
        5.2  Vermeerder / Increase R735
  
               in die verhouding / in the ratio 5 : 9
  
               R5 word / becomes R9.
  
                                                    9
               R1 word / becomes R ──
                                                    5
  
               R375 word / becomes
  
                                9         735
                           R ──  X  ────
                                5           1
  
               d.w.s. / i.e.  R 1 323            [ 5.2 ]
  
  
  
OF / OR

  
               R5 word / becomes R9
  
               R735 word / becomes Rx
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                               5           735
                                            ───  =  ────
                                               9             x
  
               Vereenvoudig  :  5 X x  =  9 X 735
  
                                              5x  =  6 615
  
                                                x  =  1 323
  
                Die vermeerderde bedrag /
  
                The increased amount is R 1 323.
  
                                                            [ 5.2 ]
  
  
  
        5.4  Vermeerder / Increase 28,4 kg
  
               in die verhouding / in the ratio 4 : 3
  
               4 kg word / becomes 3 kg.
  
                                                    3
               1 kg word / becomes  ──  kg
                                                    4
  
               28,4 kg word / becomes
  
                          3         28,4
                        ──  X  ────  kg
                          4           1
  
                         d.w.s. / i.e.  21,3  kg
  
                                                           [ 5.4 ]
  
  
  
OF / OR

  
               4 kg word / becomes 3 kg
  
               28,4 kg word / becomes x kg
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                               4           28,4
                                            ───  =  ────
                                               3             x
  
               Vereenvoudig   :  4 X x  =  3 X 28,4
  
                                               4x  =  85,2 
  
                                                 x  =  21,3
  
                Die verminderde massa /
  
                The decreased mass is 21,3 kg.
  
                                                          [ 5.4 ]
  
  
  
        5.6  Vermeerder / Increase 34,2 ℓ
  
               in die verhouding / in the ratio 9 : 5
  
               9 ℓ word / becomes 5 ℓ.
  
                                                 5
               1 ℓ word / becomes  ──  ℓ
                                                 9
  
               34,2 ℓ word / becomes
  
                           5         34,2
                         ──  X  ────  ℓ
                           9           1
  
                  d.w.s. / i.e.  19  ℓ               [ 5.6 ]
  
  
  
  
OF / OR

  
               9 ℓ word / becomes 5 ℓ
  
               34,2 ℓ word / becomes x ℓ
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                               9           34,2
                                            ───  =  ────
                                               5             x
  
               Vereenvoudig   :  9 X x  =  5 X 34,2
  
                                               9x  =  171 
  
                                                 x  =  19
  
                Die verminderde volume /
  
                The decreased volume is 19 ℓ.
  
                                                         [ 5.6 ]
  
  
  
        5.1  Increase 82 kg in the ratio 4 : 5
  
               4 kg must become 5 kg.
  
                                               5
               1 kg must become ── kg.
                                               4
  
                                                 5          82
               82 kg must become ──  X  ───    kg.
                                                 4           1
  
                                         i.e.  102,5  kg
  
                The increased mass is 102,5 kg.
  
  
  
  
                               OR
  
               If the old mass = 4 kg then
  
               the new mass = 5 kg
  
               If the old mass = 82 kg then
  
               the new mass = x kg
  
                   old mass             4          82
               ─────────  =  ───  =  ───
                  new mass             5           x
  
               Simplify  :  4 X x  =  5 X 82
  
                                      4x  =  410
  
                                        x  =  102,5
  
                The increased mass is 102,5 kg.
  
                                                           [ 5.1 ]
  
  
  
        5.3  Vermeerder / Increase 21,7 m
  
               in die verhouding / in the ratio 7 : 11
  
               7 m word / becomes 11 m.
  
                                                  11
               1 m word / becomes  ──  m
                                                   7
  
               21,7 m word / becomes
  
                         11        21,7
                        ──  X  ────  m
                          7           1
  
                  d.w.s. / i.e.  34,1  m             [ 5.3 ]
  
  
  
                               OF / OR
  
  
               7 m word / becomes 11 m
  
               21,7 word / becomes x m
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                               7          21,7
                                            ───  =  ───  
                                              11           x
  
               Simplify  :             7 X x  =  11 X 21,7
  
                                                7x  =  238,7 
  
                                                  x  =  34,1 m
  
                Die vermeerderde lengte /
  
                The increased length is 34,1 m.
  
                                                           [ 5.3 ]
  
  
  
        5.5  Vermeerder / Increase R324
  
               in die verhouding / in the ratio 8 : 5
  
               R8 word / becomes R5.
  
                                               5
               R1 word / becomes  ──
                                               8
  
               R324 word / becomes
  
                                5         324
                           R ──  X  ────
                                8           1
  
               d.w.s. / i.e.  R 202,5 
  
                                                           [ 5.5 ]
  
  
  
OF / OR

  
                 R8 word / becomes R5
  
                 R324 word / becomes Rx
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                               8          324
                                            ───  =  ───  
                                               5            x
  
               Vereenvoudig  :   8 X x  =  5 X 324
  
                                                8x  =  1 620
  
                                                  x  =  R202,5 m
  
                Die vermeerderde bedrag /
  
                The increased amount is R 202,5
  
                                                             [ 5.5 ]
  
  
  
        5.7  Vermeerder / Increase 220 volt
  
               in die verhouding / in the ratio 55 : 3
  
               55 V word / becomes 3 V.
  
                                                    3
               1 V word / becomes  ───  V
                                                   55
  
               220 V word / becomes
  
                           3           220
                        ───  X  ────  V
                          55            1
  
                d.w.s. / i.e.  12 V                   [ 5.7 ]
  
  
  
  
OF / OR

  
               55 V word / becomes 3 V
  
               220 V word / becomes x V
  
               Die verhouding bly dieselfde /
  
               The ratio remains the same.
  
                                              55        220
                                            ───  =  ───  
                                               3            x
  
               Vereenvoudig  :  55 X x  =  3 X 220
  
                                               55x  =  660
  
                                                   x  =  12
  
                Die vermeerderde volt /
  
                The increased volt is 12  V
  
                                                             [ 5.7 ]
  
  
-
  
 Antwoorde / Answers 6 
  
  
              Seuns / boys : dogters / girls = 8 : 7
  
               15 (8 + 7)  leerlinge / pupils  :
  
                                       8 seuns / boys
  
                                            8
               Seuns / Boys  =  ─── X 45  =  24
                                           15
  
             Dogters / Girls  =  45 ─ 24  =  21
  
               Daar is 24 seuns en 21 dogters
  
               in die klas. /
  
               There are 24 boys and 21 girls
  
               in the class.
  
                                                       [ 6. ]
  
  
  
          Seuns / boys : dogters / girls = 8 : 7
  
           15 (8 + 7)  leerlinge / pupils  :
  
                                       7 dogters / girls
  
                                             7
               Dogters / Girls  =  ───  X  45    =  21
                                            15
  
                 Seuns / Boys  =  45 ─ 21  =  24
  
               Daar is 24 seuns en 21 dogters
  
               in die klas. /
  
               There are 24 boys and 21 girls
  
               in the class.
  
                                                              [ 6. ]
  
  
  
 Antwoorde / Answers 7 
  
  
            7.1  Seuns / boys = 23, dogters / girls = 22
  
                       seuns / boys            23
                     ──────────  =  ────
                      dogters / girls           22
  
  
                   Dit is die eenvoudigste verhouding
  
                   want 23 is 'n priemgetal en het nie
  
                   ander faktore nie. /
  
                   It is the simplest ratio because
  
                   23 has no other factors.
  
                                                          [ 7.1 ]
  
  
  
            7.3  Seuns / boys : dogters / girls = 6 : 5
  
               11 (6 + 5)  leerlinge / pupils  :
  
                                               6 seuns / boys
  
                                             6
                 Seuns / Boys  =  ───  X  44    =  24
                                            11
  
               Dogters / Girls  =  44 ─ 24  =  20
  
                 Daar is 24 seuns en 20 dogters
  
                 in die klas. /
  
                 There are 24 boys and 20 girls
  
                 in the class.
  
                 Daar is 24 ─ 23 = 1 seun toegelaat en
  
                 22 ─ 20 = 2 dogters het die klas verlaat.
  
                 24 ─ 23 = 1 boy was admitted and
  
                 22 ─ 20 = 2 girls left the class.
  
                                                            [ 7.3 ]
  
  
  
            7.2  Seuns / boys = 23, dogters / girls = 22
  
                     Seuns / Boys = 23 ─ 3  =  20
  
                     Dogters / Girls = 22 + 4  =  26
  
  
                       seuns / boys          20         10
                     ──────────  =  ───  =  ───
                      dogters / girls         26          13
  
  
  
  
  
                                                            [ 7.2 ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   Antwoorde / Answers 8 
    
  
                     rooi : groen: geel  =  3 : 4 : 5 
  
                     Van 12 (3 + 4 + 5) lekkers,
  
                     is 3 rooi, 4 groen en 5 geel
  
                          3
                        ───  van die lekkers
                         12
  
  
                      is rooi en dit is 12
  
                        3            x
                     ───  X  ───  =  12
                       12          1
  
  
                                     3x  =  144
  
                                      x  =  48
  
                 Daar is 48 lekkers in die blik.
  
                        4
                     ───  van die lekkers is groen
                       12
  
  
                        4
                     ───  X  48    =  16
                       12
  
  
                     Daar is 16 groen lekkers en
  
                     12 rooi lekkers in die blik.
  
                     Aantal geel  =  48 ─ (12 + 16)
  
                                       =  20
  
                     Daar is 12 rooi, 16 groen en
  
                     20 geel lekkers in die blik.
  
                                                           [ 8. ]
  
  
  
                     red  :  green  :  yellow  =  3 : 4 : 5 
  
                     Of 12 (3 + 4 + 5) sweets,
  
                     3 are red, 4 green and 5 yellow
  
                             3
                           ───  of the sweets 
                            12
  
  
                             are red and that is 12
  
                        3            x
                     ───  X  ───  =  12
                       12          1
  
  
                                       3x  =  144
  
                                         x  =  48
  
                     There are 48 sweets in the tin.
  
                        4
                     ───  of the sweets are green
                       12
  
  
                        4
                     ───  X  48    =  16
                       12
  
  
                     There are 16 green sweets and
  
                     12 red sweets in the tin.
  
                     Number of yellow = 48 ─ (12 + 16)
  
                                                =  20
  
                     There are 12 red, 16 green and
  
                     20 yellow sweets in the tin.
  
                                                               [ 8 ]
  
  
  
   Antwoorde / Answers 9 
    
  
          9.1  Die verhouding 3 : 2 : 1 stel die
  
                  verhouding van die plantvoedsels,
  
                  stikstof (N), fosfor (P)
  
                  en kalium (K), voor.
  
                  Die verhouding word geskryf
  
                         N : P : K = 3 : 2 : 1.
  
                  Die 22 stel die totale persentasie
  
                  van die plantvoedsels,
  
                  N, P en K, in die sak
  
                  kunsmis voor.
  
                                                         [ 9.1 ]
  
  
  
          9.2  Massa / mass  = 22% X 10 kg
  
                                                 22
                  Massa / mass  = ────  X  10  kg
                                               100
  
                                          = 2,2  kg
  
                                                        [ 9.2 ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
          9.1  The ratio 3 : 2 : 1 represents the ratio
  
                  of the plant nutrients, nitrogen (N),
  
                  phosphorus (P) and potassium (K).
  
                  The ratio is written
  
                         N : P : K = 3 : 2 : 1.
  
                  The 22 represents the total percentage
  
                  of the plant nutrients, N, P en K,
  
                  in the bag of fertilizer.
  
                                                           [ 9.1 ]
  
  
  
          9.3  6 (3+2+1) kg bevatt / contains 3 kg N
  
                                                     3
                  1 kg bevat / contains ──  kg   N
                                                     6
  
                                                       3       2,2
                  2,2 kg bevat/contains ── X ───  kg N
                                                       6         1
  
                                          d.i. / i.e.  1,1  kg N
  
  
                                                      2        2,2
                  2,2 kg bevat/contains ── X ─── kg P
                                                      6         1
  
                                        d.i. / i.e.  0,733  kg P
  
  
                  Massa / mass K  :
  
                  M(K)  = 2,2 ─ (1,1 + 0,733) kg
  
                           =  0,367  kg
  
                  Sak bevat / Bag contains  1,1 kg N,
  
                   0,733 kg P en / and 0,367 kg K
  
                                                           [ 9.3 ]
  
  
  
   Antwoorde / Answers 10 
    
  
          10.1  
        pppervlakte / area : volume = 5,2 m2 : 1 ℓ
  
               5,2 m2 benodig / is covered by 1 ℓ
  
                                                                  1
                1 m2 benodig / is covered by ────  ℓ
                                                                5,2
  
                                                             1        20,8
        20,8 m2 benodig/is covered by ─── X ──── ℓ
                                                           5,2         1
  
                                               d.i. / i.e.  4 ℓ
  
  
            4 ℓ verf word benodig / paint is needed
  
                                                         [ 10.1 ]
  
  
  
          10.3  
  
        oppervlakte/area : volume = 11,5 m2 : 2,5 ℓ
  
       11,5 m2 benodig/is covered by 2,5 ℓ  verf/paint
  
                                                             2,5
              1 m2 benodig/is covered by ────  ℓ
                                                            11,5
  
                                                    2,5          21,4
       21,4 m2 benodig/needs by ──── X ──── ℓ
                                                   11,5          1
  
                                         d.i. / i.e.  4,652 ℓ
  
  
  
  
          10.2
  
          oppervlakte/area : volume = 17,6 m2 : 2,8 ℓ
  
            2,8 ℓ bedek / covers 17,6 m2
  
                                               17,6
              1 ℓ bedek / covers   ────  m2
                                                2,8
  
                                               17,6          5,8
           5,8 ℓ bedek / covers   ──── X ────   m2
                                                2,8             1
  
                               d.i. / i.e.  36,457 m2
  
  
                36,457 m2 word bedek / is covered
  
                                                         [ 10.2 ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
               Die blik bevat 4,2 ℓ en dit is minder as wat benodig word. Die verf kan dus nie die
               oppervlakte bedek nie.
  
               The tin only contains 4,2 ℓ paint and that is less than what is required. The paint can
               not cover the area.
                                                                                                                                      [ 10.3 ]
  
  
  
   Antwoorde / Answers 11 
    
  
          11.1
  
      afstand/distance : volume = 254 km : 21,082 ℓ
  
             254 km benodig / needs 21,082 ℓ
  
  
                                                         21,082
                1 km benodig / needs    ──────  ℓ
                                                           254
  
                                                   21,082      613
           613 km benodig/needs  ───── X ─── ℓ
                                                     254           1
  
                                    d.i. / i.e.  50,879 ℓ
  
  
           50,879 ℓ  petrol word verbruik/is needed
  
  
  
OF / OR

  
  
  
            afstand/distance          254           613
           ───────────  =  ─────  =  ───
             volume petrol            21,082          x
  
  
                           254 X x  =  613 X 21,082
  
  
                               254x  =  12 923,2663
  
  
                                     x  =  50,879
  
  
           50,879 ℓ petrol word verbruik /
  
           50,879 ℓ petrol is needed
  
                                                      [ 11.1 ]
  
  
  
    11.2
  
    afstand/distance : volume = 254 km : 21,082 ℓ
  
     21,082 ℓ verbruik/used  254 km afgelê/travelled
  
  
                                         254
         1 ℓ verbruik/used ───── km afgelê/travelled
                                      21,082
  
  
                                            254            14,2
       14,2 ℓ verbruik/used ────── X ──── km
                                          21,082            1
  
                         d.i. / i.e.  171,084  km
  
  
            Afstand afgelê /
  
                  distance travelled = 171,084 km
  
  
  
OF / OR

  
  
          afstand / distance             254               x
         ────────────  =  ──────  =  ────
             volume petrol              21,082          14,2
  
  
                       21,082 X x  =  14,2 X 254
  
  
                           21,082x  =  3 606,8
  
  
                                      x  =  171,084
  
  
              171,084 km word afgelê/is travelled
  
                                                          [ 11.2 ]
  
  
  
   Antwoorde / Answers 12 
    
  
        12.1
                                                36
          36 minute / minutes  =  ──  uur / hours
                                                60
  
                                           = 0,6 h (uur/hours)
  
           2 uur/hours 36 minute/minutes = 2 + 0,6 h
  
                                                             = 2,6 h
   
                                                          [ 12.1 ]
  
  
  
        12.3
  
            afstand/distance         253,5            415
           ─────────── = ──────  =  ────
                 tyd  /  time               2,6                x
  
  
                       253,5 X x  =  2,6 X 415
  
  
                           253,5x  =  1 079
  
  
                                    x  =  4,256
  
  
              Tydsduur / time taken  =  4,256 h
  
                                                       [ 12.3 ]
  
   
  
                                             48
        12.2  3 h 48 min = 3 + ──  h
                                             60
  
                                 = 3,8 h
  
  
          afstand / distance            253,5             x
         ────────────  =  ──────  =  ────
                tyd  /  time                    2,6             3,8
  
  
                            2,6 X x  =  253,5 X 3,8
  
  
                                2,6x  =  963,3
  
  
                                    x  =  370,5
  
  
              Afstand afgelê /
                      distance travelled  =  370,5 km
  
                                                          [ 12.2 ]
  
  
  
  
  
  
  
  
  
   Antwoorde / Answers 13 
    
  
                Hierdie is 'n voorbeeld van omgekeerde
  
                eweredigheid want meer mans sal
  
                minder dae werk en omgekeerd, minder
  
                mans sal langer werk as almal teen
  
                dieselfde tempo werk.
  
  
                As a omgekeerd eweredig is aan b, dan
  
                sal a X b = 'n konstante, bv. a X b = 36
  
                Gestel a X b = 36. Let nou op dat
  
                as a groter word, word b in dieselfde
  
                mate kleiner.
  
                As a = 1 is b = 36 want a X b = 36
  
                As a tweemaal groter word, a = 2,
  
                dan is b = 18, b is die helfte kleiner.
  
                
  
                Maar let op dat a X b = 36.
  
                Die produk van die veranderlikes
  
                bly dieselfde.
  
  
  
        13.1  Hier is mans X dae = konstante
  
                  mans X dae = 10 X 3 = 30
  
                  6 mans werk d dae.
  
                  6 X d = 10 X 3
  
                         10 X 3
                  d = ─────    =  5
                              6
  
                  6 mans sal 5 dae werk
  
                                                           [ 13.1 ]
  
  
  
        13.2  mans/men X dae/days = 30
  
                  12 mans/men werk/word d dae/days
  
                  12 X d = 10 X 3
  
                         10 X 3
                  d = ─────    =  2,5
                            12
  
                  12 mans sal 2,5 dae we+rk /
  
                  12 men will work for 2,5 days.
  
                                                          [ 13.2 ]
  
  
  
        13.4  mans/men X dae/days = 30
  
                  m mans/men werk/work 2 dae/days
  
                  m X 2 = 10 X 3
  
                         10 X 3
                  m = ─────    =  15
                             2
  
                  15 mans sal 2 dae we+rk /
  
                  15 men will work for 2 days.
  
                                                        [ 13.4 ]
  
  
  
                This is an example of inverse proportion
  
                because more men will work less days
  
                and inversely, less men will work more
  
                days if everbody works at the same rate.
  
  
  
  
                If a is inversely proportional to b, then
  
                a X b = a constant, e.g. a X b = 36
  
                Let a X b = 36. Note that if a
  
                increases, b will decrease at the
  
                same rate.
  
                If a = 1 then b = 36 because a X b = 36
  
                If a is doubled, a = 2, then
  
                b = 18, b is halved.
  
                
  
                But note that a X b = 36.
  
                The product of the variables
  
                remain the same.
  
  
  
        13.1  Here men X days = constant
  
                  mans X dae = 10 X 3 = 30
  
                  6 men werk d days.
  
                  6 X d = 10 X 3
  
                         10 X 3
                  d = ─────    =  5
                              6
  
                  6 men will work 5 days.
  
                                                          [ 13.1 ]
  
  
  
        13.3  mans/men X dae/days = 30
  
                  m mans/men werk/work 7 dae/days
  
                  m X 7 = 10 X 3
  
                         10 X 3
                  m = ─────    =  4,28571.....
                              7
  
                  Daar bestaan nie 'n breuk van 'n
  
                  man nie en dus moet of 4 of 5
  
                  gebruik word. 4 mans sal meer as
  
                  7 dae werk en 5 mans sal minder
  
                  as 7 dae werk. /
  
                  A fraction of a man does not exist
  
                  and therefore either 4 or 5 man
  
                  must be used. 4 men will work more
  
                  than 7 days and 5 men will word
  
                  less than 7 days.
  
                                                         [ 13.3 ]
  
  
  
  
  
  
  
  
  
   Antwoorde / Answers 14 
    
  
      14.1  Hier / Here
  
        kinders/children(p) X lekkers/sweets(s) = c
  
                p X s = 20 X 8 = 160
  
                40 p kry/ get a s.
  
                40 X a = 20 X 8
  
                       20 X 8
                a = ─────    =  4
                          40
  
                40 kinders kry 4 lekkers elk. /
  
                40 children get 4 sweets each.
  
                                                          [ 14.1 ]
  
  
  
      14.3  p X s = 20 X 8 = 160
  
                m p kry/ get 16 s.
  
                m X 16 = 20 X 8
  
                        20 X 8
                m = ─────    =  10
                           16
  
                10 kinders kry 16 lekkers elk. /
  
                10 children get 16 sweets each.
  
                                                         [ 14.3 ]
  
  
  
        14.2
  
        kinders/children X lekkers / sweets = 20 X 8
  
        8 kinders kry / children get b lekkers/sweets.
  
                  8 X b = 20 X 8
  
                               20 X 8
                        b = ─────    =  20
                                    8
  
                  8 kinders kry 20 lekkers elk. /
  
                  8 children get 20 sweets each.
  
                                                         [ 14.2 ]
  
  
  
  
  
        14.4  p X s = 20 X 8
  
          q kinders kry / children get 4 lekkers/sweets.
  
                  q X 4 = 20 X 8
  
                               20 X 8
                        q = ─────    =  40
                                    4
  
                  40 kinders kry 4 lekkers elk. /
  
                  40 children get 4 sweets each.
  
                                                         [ 14.4 ]