WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Koers, verhouding en eweredigheid : antwoorde
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Rate, ratio and proportion : answers
  
  
Antwoorde / Answers  1  
  
    
         1.1  Meer aartappels sal meer kos.
                                                         [ V 1.1 ]
    
         1.2  Direkte eweredigheid.
                                                         [ V 1.2 ]
    
         1.1  More potatoes will cost more.
                                                               [ Q 1.1 ]
    
         1.2  Direct proportion
                                                               [ Q 1.2 ]
    
         1.3    4 kg aartappels kos / potatoes cost  R 28,45
  
                                                                                  28,45
                  1 kg aartappels kos / potatoes cost  R ──────
                                                                                     4
  
                                                                                  28,45
                15 kg aartappels kos / potatoes cost  R ──────  X  15
                                                                                     4
  
                                                             d.i. / i.e.  R106,69
  
  
                15 kg aartappels kos / potatoes cost R106,69                                                                       [ V / Q 1.3 ]
  
  
    
         1.4    R28,45 is die prys van / the price of 4 kg aartappels / potatoes
  
                                                                        4
                  R 1 is die prys van / price of   ──────    aartappels / potatoes
                                                                    28,45
  
                                                                               4
                  R 77,10 is die prys van / price of   ──────  X  77,10    aartappels / potatoes
                                                                            28,45
  
                                                             d.i. / i.e.  10,84 kg  
  
  
                10,84 kg aartappels kos / potatoes cost R77,10                                                                   [ V / Q 1.4 ]
  
  
  
Antwoorde / Answers  2  
  
    
         2.1    3 pampoene kos / pumpkins cost  R 38,25
  
                                                                             38,25
                  1 pampoen kos / pumpkin costs  R ──────
                                                                                3
  
                                                                               38,25
                  8 pampoene kos / pumpkins cost  R ──────  X  8
                                                                                  3
  
                                                          d.i. / i.e.  R102,00
  
  
                8 pampoene kos / pumpkins cost R102,00                                                             [ V / Q 2.1 ]
  
  
    
         2.2    R38,25 koop / buys 3 pampoene / pumpkins
  
                                                     3
                  R 1 koop / buys    ──────    pampoene / pumpkins
                                                  38,25
  
                                                            4
                  R 63,75 koop / buys   ──────  X  63,75    aartappels / potatoes
                                                        28,45
  
                                          d.i. / i.e.  5 
  
  
                5 pampoene kos / pumpkins cost R63,75                                                               [ V / Q 2.2 ]
  
  
  
Antwoorde / Answers  3  
  
    
         3.1  34,25 ℓ petrol kos R655,55
  
                                           655,55
                1 ℓ petrol kos  R ─────
                                            34,25
  
                                                  655,55
                68,21 ℓ petrol kos  R ─────  X  68,21
                                                   34,25
  
                68,21 ℓ petrol kos  R 1 305,55
  
                                                         [ V 3.1 ]
  
    
         3.2  R655,55 koop 34,25 ℓ petrol
  
                                 34,25
                R 1 koop ───── ℓ petrol
                                655,55
  
                                          34,25
                R 816,20 koop ───── X 816,20 ℓ
                                         655,55
  
                R 816,20 koop 42,643 ℓ petrol.
  
                                                         [ V 3.2 ]
  
    
         3.1  34,25 ℓ of petrol costs R655,55
  
                                                  655,55
                1 ℓ of petrol costs  R ─────
                                                   34,25
  
                                                         655,55
                68,21 ℓ of petrol costs  R ─────  X  68,21
                                                          34,25
  
                68,21 ℓ of petrol costs  R 1 305,55
  
                                                         [ Q 3.1 ]
  
    
         3.2  R655,55 buys 34,25 ℓ of petrol
  
                                 34,25
                R 1 buys ───── ℓ of petrol
                                655,55
  
                                          34,25
                R 816,20 buys ───── X 816,20 ℓ
                                         655,55
  
                R 816,20 buys 42,643 ℓ of petrol.
  
                                                         [ Q 3.2 ]
  
  
Antwoorde / Answers  4  
  
    
         4.1  9 km im 36,5 minute
  
                                   36,5
                1 km in    ─────  minute
                                     9
  
                                   36,55
                21 km in   ─────  X  21  minutes
                                      9
  
                21 km in   85,17 minute  =  1 h 25,17 m
  
                                                         [ V 4.1 ]
  
    
         4.1  9 km in 36,5 minutes
  
                                36,5
                1 km in  ───── minutes
                                   9
  
                                   36,5
                21 km in  ─────  X  21 minutes
                                      9
  
                21 km in 85,17 minutes = 1 h 25,17 m
  
                                                         [ Q 4.1 ]
  
    
         4.2    In 36,5 minute / minutes hardloop hy / he runs 9 km
  
                                                                                             9
                  In 1 minuut / minute hardloop hy / he runs  ──────  km
                                                                                          36,5
  
                                                                                                   9
                  In 55,8 minute / minutes hardloop hy / he runs  ──────  X  55,8  km
                                                                                                 36,5
  
                                                                               d.i. / i.e.  13,759  km
  
  
                In 55,8 minute / minutes hardloop hy / he runs 13,759 km                                          [ V / Q 4.2 ]
  
  
  
Antwoorde / Answers  5  
  
    
         5.1    In 33,4375 minute / minutes ry dit / it travels 53,5  km
  
                                                                                 53,5
                  In 1 minuut / minute ry dit / it travels  ───────  km
                                                                               33,4375
  
                                                                                      53,5
                  In 60 minute / minutes ry dit / it travels  ───────  X  60  km
                                                                                  33,4375
  
                                                                     d.i. / i.e.  96  km
  
  
                Spoed van mtor / Speed of car is 96 km/h                                                                  [ V / Q 5.1 ]
  
  
    
         5.2    In 33,4375 minute / minutes ry die motor / the car travels 53,5  km
  
                                                                                                       53,5
                  In 1 minuut / minute ry die motor / the car travels  ───────  km
                                                                                                    33,4375
  
                                                                                                                      53,5
                  In 3,5 X 60 minute / minutes ry die motor / the car travels  ────────  X  3,5 X 60  km
                                                                                                                  33,4375
  
                                                                                                 d.i. / i.e.  336  km
  
  
                Afstand gery / Distance traveled is 336 km                                                              [ V / Q 5.2 ]
  
  
         OF / OR
  
                  In 1 uur / hour ry die motor / the car travels 96 km    . . . . Van / From  5.1
  
                  In 3,5 uur / hours ry die motor / the car travels 96 X 3,5  km
  
                                                                               d.i. / i.e.  336  km
  
  
                Afstand gery / Distance traveled is 336 km                                                             [ V / Q 5.2 ]
  
  
    
         5.3    Die motor ry / The car travels 53,5 km in 33,4375 minute / minutes
  
                                                                                  33,4375
                  Die motor ry / The car travels 1 km in  ───────  minute / minutes
                                                                                     53,5
  
                                                                                       33,4375
                  Die motor ry / The car travels 38,7 km in  ───────  X 38,7  minute / minutes
                                                                                         53,5
  
                                                                       d.i. / i.e.  24,19  minute / minutes
  
  
                  Dit neem 24.19 minute om 38,7 km te ry.  /  It takes 24,19 minutes to travel 38,7 km.
  
                                                                                                                                                [ V / Q 5.3 ]
  
  
         OF / OR
  
                  Die motor ry / The car travels 96 km in 60 minute / minutes
  
                                                                                  60
                  Die motor ry / The car travels 1 km in  ────  minute / minutes
                                                                                  96
  
                                                                                       60
                  Die motor ry / The car travels 38,7 km in  ────  X 38,7  minute / minutes
                                                                                       96
  
                                                                       d.i. / i.e.  24,19  minute / minutes
  
  
                  Dit neem 24.19 minute om 38,7 km te ry.  /  It takes 24,19 minutes to travel 38,7 km.
  
                                                                                                                                                [ V / Q 5.3 ]
  
  
  
Antwoorde / Answers  6  
  
    
         6.1    1 brood lewer / loaf of bread gives 17 snye / slices.
  
                  6 brode lewer / loaves of bread give 6 X 17 snye / slices.
  
                                                               d.i. / i.e.  102 snye / slices
  
                  3 snye / slices voed / feeds 1 kind / child.
  
                                                            1
                  1 sny / slice voed / feeds ── kind / child.
                                                            3
  
                                                                    1
                  102 snye / slices voed / feeds ──  X  102  kinders / children.
                                                                    3
  
                                                  d.i. / i.e.   34  kinders / children                                              [ V / Q 6.1 ]
  
  
  
Antwoorde / Answers  7  
  
    
         7.1  meer liter is nodig                       [ V 7.1 ]
    
         7.2  Direkte eweredigheid                  [ V 7.2 ]
    
         7.1  More liters                        [ Q 7.1 ]
    
         7.2  Direct proportion              [ Q 7.2 ]
    
         7.3    31,947 km  gebruik / uses   2,3  ℓ
  
                                                                   2,3
                         1  km   gebruik / uses   ──────     ℓ
                                                                31,947
  
                                                                    2,3
                     100  km   gebruik / uses   ──────  X  100   ℓ
                                                                 31,947
  
                                                    d.i. / i.e.  7,199  ℓ
  
  
                  7,199  ℓ  word benodig / is needed.                                                                            [ V / Q 7.3 ]
  
  
    
         7.4      2,3 ℓ  is nodig vir / needed for  31,947  km
  
                                                                             2,3
                       1  ℓ  is nodig vir  / needed for   ──────   km
                                                                          31,947
  
                                                                             2,3
                  18,6  ℓ  is nodig vir  / needed for   ──────   X 18,6  km
                                                                          31,947
  
                                                    d.i. / i.e.  258,354  km
  
  
                  Afstand is  /  Distance is  258,354 km                                                                   [ V / Q 7.4 ]
  
  
  
Antwoorde / Answers  8  
  
    
         8.1  1 koppie = 147 g
                2 koppies = 147 X 2 g
                                = 294 g < 300 g
                Sy het genoeg meel.           [ V 8.1 ]
    
         8.2  1 koppie melk = 250 mℓ
                ½ koppie = 250 X ½ mℓ
                                = 125 mℓ             [ V 8.2 ]
    
         8.1  1 cup = 147 g
                2 cups = 147 X 2 g
                            = 294 g < 300 g
                She has enough flour.           [ Q 8.1 ]
    
         8.2  1 cup of milk = 250 mℓ
                ½ cups = ½ X 250 mℓ
                            = 125 mℓ                     [ Q 8.2 ]
    
         8.3    1  teelepel / teaspoon  =  5  mℓ
  
                  3  teelepels / teaspoons  =  3 X 5  mℓ
  
                                                          =  15  mℓ
  
                  250 mℓ  suiker weeg / sugar weighs  200  g
  
                                                                               200
                      1 mℓ  suiker weeg / sugar weighs  ────  g
                                                                               250
  
  
                                                                               200
                    15 mℓ  suiker weeg / sugar weighs  ────  X  15  g
                                                                               250
  
                                                                d.i. / i.e.  12  g
  
  
                  Sy het 12 g suiker nodig  /  She needs 12 g of sugar.                                            [ V / Q 8.3 ]
  
  
    
                               5
         8.4      T  =   ── ( 450  ─  32 )  °C
                               9
  
                        =  232,22  °C                                                                                                     [ V / Q 8.4 ]