WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Finansiële documente, tariewe : antwoorde
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Financial documents, tariffs : answers
  
  
Antwoorde  / Answers  1  
  
    
        1.1.1   Van 0 tot 6 kl: gratis en
                   van 7 tot 8 kl R2/kl
                                                                 [ V 1.1 ]
    
        1.1.2   Van 0 tot 6 kl: gratis en
                   van 7 tot 8 kl R2/kl
                   d.i. koste = R(6 x 0 + 2 x 2) = R4,00
                                                                 [ V 1.1 ]
    
        1.1.1   From 0 to 6 kl: free and
                   from 7 to 8 kl R2/kl
                                                                 [ Q 1.1 ]
    
        1.1.2   From 0 to 6 kl: free and
                   from 7 to 8 kl R2/kl
                   i.e. cost = R(6 x 0 + 2 x 2) = R4,00
                                                                 [ Q 1.1 ]
    
        1.2   49,12 kl word benader tot / is rounded up to 50 kl.
               Bedrag betaalbaar / Amount due = R(6 x 0 + (29 - 6) x 2 + (49 - 30) x 2,40 + 2 x 3,50)
                                                                    = R98,60                                                              [ V/Q 1.2 ]
    
        1.3   Bedrag betaalbaar / Amount due = R(6 x 0 + (29 - 6) x 2 + (49 - 30) x 2,40 + 7 x 3,50)
                                                                     = R116,10
                Die rekenig is dus verkeerd - dit is te groot / The account is thus wrong - it is in excess.
                Bedrag te groot  Amount in excess  =  R135,65 ─ R116,10
                                                                         =  R 19,55                                               [ V/Q 1.3 ]

  
Antwoorde  / Answers  2  
  
    
        2.1   Totale uitgawe = R8 520,00
                Nee, die uitgawe is
                R(8 520 - 7 600) = R920
                meer as die inkomste.
                                                                 [ V 2.1 ]
    
        2.2   Nog nie. Die uitgawe is nog
                R420 meer as die inkomste.
                Gert kan afskaal op vermaak en
                klere. Spandeer R200 minder op
                klere en R420 op vermaak.
                Dan klop die begroting.
                                                                 [ V 2.2 ]
    
        2.3   Spandeer R300 op klere,
                vermaak inkort tot R200 en
                motor onderhoud inkort met R20.
                                                                 [ V 2.3 ]
    
        2.1   Total expenses = R8 520,00
                No, the expenses are
                R(8 520 - 7 600) = R920
                more than the income.
                                                                 [ Q 2.1 ]
    
        2.2   Not yet. The expenses are still
                in excess by R420 over the income.
                Jack can spend less on entertainment
                and clothes. Spend R200 less on
                clothes and R420 on entertainment.
                Then the budget balances.
                                                                 [ Q 2.2 ]
    
        2.3   Spend R300 on clothes,
                decrease entertainment by R200
                and motor maintenance by R20.
                                                                 [ Q 2.3 ]
  
Antwoorde  / Answers  3  
  
    
        3.1   A = R17 000 en B = R18 300
                                                                 [ V 3.1 ]
    
        3.1   Koos kan nie al sy uitgawes
                bekostig nie, want die uitgawes
                oorskry die inkomste met R1 300.
                                                                 [ V 3.2 ]
    
        3.3   Die tekort is R1 200. Besnoei
                R500 op klere en R500 op
                vermaak en R200 op motor
                onderhoud - ry minder,
                spaar op brandstof.
                                                                 [ V 3.3 ]
    
        3.1   A = R17 000 and B = R18 300
                                                                 [ Q 3.1 ]
    
        3.2   Peter cannot afford all his expenses,
                because the expenses exceed
                the income by R1 300.
                                                                 [ Q 3.2 ]
    
        3.3   The shortage is R1 200. Cut down
                expenses by spending R500
                less on clothes, R500 on
                entertainment and R200 on
                on fuel, use the car less.
                                                                 [ Q 3.3 ]
  
Antwoorde  / Answers  4  
  
    
        4.1   Die foonnommer is 001 968 0001.
                                                                 [ V 4.1 ]
    
        4.2   Die posadres is
                Bus 34, Komhier 001908
                                                                 [ V 4.2 ]
    
        4.3   Die datum van die faktuur / rekening
                28 / 03/ 2016.
                                                                 [ V 4.3 ]
    
        4.4   Laaste datum vir betaling
                is 14/04/2016.
                                                                 [ V 4.4 ]
    
        4.5   Die rekening is betaal en dus
                moet daardie bedrag afgetrek
                word sodat die uitstaande
                bedrag R0,00 is.
                                                                 [ V 4.5 ]
    
        4.6   Water verbruik = (1241 - 1206) kl
                                        = 35 kl
                en elektrisiteit = (8324 - 80136)
                                       = 188 eenhede
                                                                 [ V 4.6 ]
    
        4.7   Bedrag = R(6 x 0 + (35 - 6) x 1,10)
                            = R31,90
                BTW = R31,90 x 0,14 = R4,47
                en dus is
                Totale koste = R31,90 + R4,47
                = R36,37
                Die rekening is dus heel verkeerd.
                                                                 [ V 4.7 ]
    
        4.8   Elektrisiteit verbruik is 188 eenhede
                en nie 288 nie. Die koste is dus
                verkeerd.
                Koste = R188 x 1,45 = R272,60
                sodat BTW = R272,60 x 0,14
                                   = R38,16 en
                Totaal = R310,76.
                Die bedrag betaalbaar is dus
                verkeerd. Die bedrae moet wees :
                Bedrag = R424,50; BTW = R59,43
                en Bedrag = R894,05
                                                                 [ V 4.8 ]
    
        4.9   Nee. Teen 1,6% is die belasting
                R350 000 x 0,016 = R5 600,00.
                Die belasting van R4 921,44 word
                bereken teen (4921,44 ÷ 350000) x 100
                                                     = 1,406%
                                                                 [ V 4.9 ]
    
        4.1   The phone number is 001 968 0001.
                                                                 [ Q 4.1 ]
    
        4.2   The postal addres is
                P. O. Box 34, Hereweare 001908
                                                                 [ Q 4.2 ]
    
        4.3   The invoice is dated
                28 / 03 / 2016.
                                                                 [ Q 4.3 ]
    
        4.4   Last date for payment is
                14/04/2016.
                                                                 [ Q 4.4 ]
    
        4.5   The account is settled and thus
                that amount must be deducted
                from the account balance so that
                the outstanding amount is R0,00.
                                                                 [ Q 4.5 ]
    
        4.6   Water consumed = (1241 - 1206) kl
                                            = 35 kl
                and electricity = (8324 - 80136)
                                       = 188 units
                                                                 [ Q 4.6 ]
    
        4.7   Amount = R(6 x 0 + (35 - 6) x 1,10)
                             = R31,90
                VAT = R31,90 x 0,14 = R4,47
                so that
                Total cost = R31,90 + R4,47
                                = R36,37
                The account is completely in error.
                                                                 [ Q 4.7 ]
    
        4.8   Electricity consumption is
                188 units and not 288. The cost
                is therefore erroneous.
                Cost = R188 x 1,45 = R272,60
                so that VAT = R272,60 x 0,14
                                   = R38,16 and
                Total = R310,76.
                The amount due is therefore wrong.
                The amounts should be :
                Amount = R424,50; VAT = R59,43
                and Amount = R894,05
                                                                 [ Q 4.8 ]
    
        4.9   No. At 1,6% the levy is
                R350 000 x 0,016 = R5 600,00.
                The levy of R4 921,44 is calculated
                at (4921,44 ÷ 350000) x 100
                                    = 1,406%
                                                                 [ Q 4.9 ]
  
Antwoorde  / Answers  5  
  
    
        5.1   Die datum is 2 Mei 2005 en die
                nommer van die staat is 51.
                                                                 [ V 5.1 ]
    
        5.2   Die kommas word gebruik as
                honderde en duisende skeiers en
                die punte word gebruik as
                die desimale skeiers.
                                                                 [ V 5.2 ]
    
        5.3   Die rentekoers is 1% per jaar
                of 0,083333% per maand.
                                                                 [ V 5.3 ]
    
        5.4   Die rente verdien = Pi
                          = R1 986.32 x 0.00083333
                          = R1.66
                                                                 [ V 5.4 ]
    
        5.5   Dit beteken dat die rente verdien
                by die Saldo, geld in die rekening,
                of kapitaal gevoeg word.
                                                                 [ V 5.5 ]
    
        5.6   Saldo = R1,985.32 + 1.66
                          = R1,987.98
                                                                 [ V 5.6 ]
    
        5.7   Die bedrae in die Debiete kolom
                is die bedrae wat sekere dinge
                betaal of geld wat uit die
                rekening onttrek word.
                Die Saldo word dus met
                daardie bedrag verminder.
                                                                 [ V 5.7 ]
    
        5.8   Die rente verdien = I
                        = R1,168.78 x 0.00083333
                        = R0.97
                sodat die Saldo = R1,169.75
                                                                 [ V 5.8 ]
    
        5.1   The date is May 2, 2005 and the
                number of the statement is 51.
                                                                 [ Q 5.1 ]
    
        5.2   The commas are used to separate
                hundreds and thousands and the
                fullstops are used to separate
                the integers from the decimals.
                                                                 [ Q 5.2 ]
    
        5.3   The interest rate is 1% per annum
                or 0,083333% per month.
                                                                 [ Q 5.3 ]
    
        5.4   The interest earned = Pi
                                = R1 986.32 x 0.00083333
                                = R1.66
                                                                 [ Q 5.4 ]
    
        5.5   It means that the interest earned
                is added to the Balance to form
                the new Capital.
                                                                 [ Q 5.5 ]
    
        5.6   Balance = R1,985.32 + 1.66
                              = R1,987.98
                                                                 [ Q 5.6 ]
    
        5.7   The amounts in the Debit column
                are the amounts that are
                withdrawn from the Balance to
                pay other accounts or fees.
                The Balance is therefore
                decreased by that amount.
                                                                 [ Q 5.7 ]
    
        5.8   The interest earned = I
                              = R1,168.78 x 0.00083333
                              = R0.97
                so that the Balance = R1,169.75
                                                                 [ Q 5.8 ]
  
Antwoorde  / Answers  6  
  
    
        6.1   Die datum is 2 Mei 2005 en die
                nommer van die staat is 251.
                                                                 [ V 6.1 ]
    
        6.2   Die Saldo oorgebring is 'n bedrag
                wat Mej. Marais aan die Bank skuld
                - haar rekening is oortrokke -
                sy leen geld by die Bank.
                                                                 [ V 6.2 ]
    
        6.3   Die bedrae in die Debiete kolom
                is die bedrae wat sekere dinge
                betaal of geld wat uit die rekening
                onttrek word. Geld word uit die
                rekening verwyder en daarom
                moet die Saldo dus met
                daardie bedrag verminder.
                                                                 [ V 6.3 ]
    
        6.4   Saldo = R3,814.21- + R7,420.00
                          = R3,605.79
                Die teken is positief wat beteken
                dat die rekening nie meer
                oortrokke is nie, daar is weer
                fondse in die rekening.
                                                                 [ V 6.4 ]
    
        6.5   Saldo = R20.96-
                Die rekening is weer met
                R20.96 oortrokke.
                                                                 [ V 6.5 ]
    
        6.6   Saldo = R2,451.21-
                                                                 [ V 6.6 ]
    
        6.7   Saldo = R2,4763.21-
                Daar is nou R800 in die
                rekening in betaal wat die
                oortrokke rekening verminder.
                                                                 [ V 6.7 ]
    
        6.8   Saldo = R4,423.76-
                                                                 [ V 6.8 ]
    
        6.9   P = R4,423.76- + 99.00-
                    = R4,522.76- en
                  i = 13,5 ÷ (100 x 12)
                    = 0.01125
                  I = Pi = R4,522.76 x 0.01125
                    = R50.88
                                                                 [ V 6.9 ]
    
        6.10   Saldo = R4,522.76- + (R50.88-)
                            = R4,573.64-
                                                                 [ V 6.10 ]
    
        6.1   The date is May 2, 2005 and
                the number of the statement is 251
                                                                 [ Q 6.1 ]
    
        6.2   The Balance brought forward is an
                amount that Miss Marais owes
                the Bank - her account is overdrawn
                - she "borrows" money from the Bank.
                                                                 [ Q 6.2 ]
    
        6.3   The amounts in the Debits column
                are the amounts that were used to
                pay certain other debts or cash
                withdrawals. Money is withdrawn
                from the account and therefore the
                Balance must be decreased by
                that amount.
                                                                 [ Q 6.3 ]
    
        6.4   Balance = R3,814.21- + R7,420.00
                = R3,605.79
                The sign is positive which means
                that the account is no longer
                overdrawn, there is "money in
                the Bank", there are funds available.
                                                                 [ Q 6.4 ]
    
        6.5   Balance = R20.96-
                The account is once more
                overdrawn by R20.96.
                                                                 [ Q 6.5 ]
    
        6.6   Balance = R2,451.21-
                                                                 [ Q 6.6 ]
    
        6.7   Balance = R2,4763.21-
                An amount of R800 is deposited
                into the account which decreases
                the amount overdrawn.
                                                                 [ Q 6.7 ]
    
        6.8   Balance = R4,423.76-
                                                                 [ Q 6.8 ]
    
        6.9   P = R4,423.76- + 99.00-
                    = R4,522.76- and
                  i = 13,5 ÷ (100 x 12)
                    = 0.01125
                  I = Pi = R4,522.76 x 0.01125
                    = R50.88
                                                                 [ Q 6.9 ]
    
        6.10   Balance = R4,522.76- + (R50.88-)
                                = R4,573.64-
                                                                 [ Q 6.10 ]
  
Antwoorde  / Answers  7  
  
    
        7.1   20 items is gekoop.
                                                                 [ V 7.1 ]
    
        7.2   4 plastiese drasakke is gekoop.
                                                                 [ V 7.2 ]
    
        7.3   24 liter.                                     [ V 7.3 ]
    
        7.4   6 items is BTW vry.                  [ V 7.4 ]
    
        7.5   R109,70                                     [ V 7.5 ]
    
        7.6   R146,45                                     [ V 7.6 ]
    
        7.7   R10,99                                     [ V 7.7 ]
    
        7.1   20 items were bought.
                                                                 [ Q 7.1 ]
    
        7.2   4 plastic carry bags were bought.
                                                                 [ Q 7.2 ]
    
        7.3   24 liter                                      [ Q 7.3 ]
    
        7.4   6 items are VAT free.               [ Q 7.4 ]
    
        7.5   R109.70                                    [ Q 7.5 ]
    
        7.6   R146.45                                    [ Q 7.6 ]
    
        7.7   R10,99                                      [ Q 7.7 ]
  
  
    
        7.8   0,96 kg   kos / costs R34,56
  
                                                    R34,56
                     1 kg   kos / costs  ──────    
                                                      0,96
  
                                                = R36,00                                                                          [ V/Q 7.8 ]
  
  
    
        7.9   18 eiers / eggs   kos / costs R29,99
  
                                                               R29,99
                     1 eier / egg   kos / costs  ──────    
                                                                   18
  
                                             d.i. / i.e.  R1,6661111
  
  
                     6 eiers / eggs   kos / costs R9,99
  
                                                                R9,99
                     1 eier / egg   kos / costs  ──────    
                                                                   6
  
                                              d.i. / i.e.  R1,665186
  
  
                 Die 6 eier verpakking is dus effens goedkoper. / The 6 egg pack is thus a little cheaper.
  
                                                                                                                                                [ V/Q 7.9 ]
    
        7.10   0,75 kg wortels kos / carrots costs   R11,24
  
                                                                              R11,24
                     1 kg wortels / carrots   kos / costs  ──────    
                                                                                0,75
  
                                                            d.i. / i.e.  R14,98666667
  
  
                     3 kg wortels / carrots   kos / costs   3 X R 14,98666667
  
                                                                              = R44,96
                                                                                                                                                [ V/Q 7.10 ]
  
Antwoorde  / Answers  8  
  
    
        8.1  
Tyd / Time (minute / minutes) 0 10 50 200 250 300 400
Koste / Cost (R) 0 5 25 100 125 150 200
  
                                                                                                                                         [ V 8.1 ]
  
                                                           Koste
        8.2   Ja, want die verhouding  ──────  
                                                             tyd
  
                bly konstant
                                                                 [ V 8.2 ]
  
  
                                                         Cost
        8.2   Yes, because the ratio  ──────  
                                                         time
  
                remains constant / the same
                                                                 [ Q 8.2 ]
      
        8.3   Sien die grafiek langsaan.
                                                                 [ V 8.3 ]
      
        8.3   See the graph in 8.3
                                                                 [ V 8.3 ]
      
        8.4.1   A; R50                                   [ V 8.4.1 ]
      
        8.4.2   B; 200 minute / minutes        [ V 8.4.2 ]
      
        8.4.3   C; R75                                   [ V 8.4.3 ]
      
        8.4.4   D; 250 minute / minutes        [ V 8.4.4 ]
  
    
        8.5   Die lyn sal opwaarts skuif met
  
                die helfte van die oorspronklike
  
                y-waarde (Koste-waarde),
  
                bv. by 100 minute sal die punt
  
                met die helfte van R50,
  
                d.w.s. R25, opskuif sodat
  
                die nuwe Koste nou R75 is.
  
                Sien grafiek in 8.5
  
                                                                 [ V/Q 8.5 ]
  
    
        8.5   The line will shift upwards by half
  
                of the original y-value
  
                (Cost-value),
  
                e.g. at 100 minutes the point
  
                will shift upwards by half of R50,
  
                i.e. R25, so that the new Cost
  
                is now R75.
  
                See the graph in 8.5
  
                                                                 [ V/Q 8.5 ]
  
  
        8.3
  
  
                                                                 [ V/Q 8.3 ]
  
  
        8.5
  
  
                                                                 [ V/Q 8.5 ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Antwoorde  / Answers  9  
  
             9.1   Die grafiek begin in die
  
                     punt (0 ; 50). Daar is nou
  
                     'n vaste R50 koste wat
  
                     onafhanklik van die tyd is.
  
                                                                 [ V 9.1 ]
  
  
             9.2.1   R90,00                            [ V 9.2.1 ]
  
  
             9.2.2   120 minute                      [ V 9.2.2 ]
  
  
             9.2.3   R120,00                          [ V 9.2.3 ]
  
  
             9.2.4   310 minute                      [ V 9.2.4 ]
  
  
  
             9.1   The graph starts at the point
  
                     (0 ; 50). There is now a fixed
  
                     cost that is independent of
  
                     the time.
  
                                                                 [ Q 9.1 ]
  
  
             9.2.1   R90,00                            [ Q 9.2.1 ]
  
  
             9.2.2   120 minute                      [ Q 9.2.2 ]
  
  
             9.2.3   R120,00                          [ Q 9.2.3 ]
  
  
             9.2.4   310 minute                      [ Q 9.2.4 ]
  
  
  
             9.3   Die vaste fooi van R50 moet afgetrek word van die R150 om die koste vir 250 minute te kry.
  
                     The fixed cost of R50 must be deducted from thr R150 to calculate the cost for 250 minutes.
  
  
                                                                                            R100
                     Koste per minuut / Cost per minute  = ————————  = R0,40
                                                                                    250 minute(s)                                                        [ V/Q 9.3 ]
  
             9.4   9.2.1  Koste / Cost  =  R50 + (0,40 x 100)    =  R(50 + 40)    =  R90,00
  
  
                                                           R50
                     9.2.2  Tyd / Time  =  ──────  = 125 minute(s)
                                                         R0,40
  
  
                     9.2.3  Koste / Cost  =  R50 + (0,40 x 150) = R(50 + 60) = R110,00
  
  
                     9.2.4  Koste vir minute gepraat = R(178 - 50) = R128
  
                                                        R128
                              Tyd / Time  =  ──────  = 320 minute(s)
                                                       R0,40                                                                                               [ V/Q 9.4 ]
  
  
Antwoorde  / Answers  10  
  
             10.1   Die grafiek begin by
  
                       punt (0 ; 50). Daar is nou
  
                       'n vaste R50 koste wat
  
                       onafhanklik van die tyd is.
  
                                                                 [ V 10.1 ]
  
  
             10.2   Van A na B is die grafiek
  
                       ewewydig aan die horisontale
  
                       tyd-as sodat daar geen
  
                       verandering in waarde op
  
                       die vertikale koste-as is nie
  
                       alhoewel die tyd toeneem,
  
                       d.w.s. van A na B bly die
  
                       koste konstant op R50
  
                       alhoewel die tyd toeneem
  
                       van 0 tot 100 minute.
  
                                                                   [ V 10.2 ]
  
  
             10.3   Van B na C is die grafiek
  
                       skuins sodat die waardes op
  
                       die vertikale koste-as toeneem
  
                       soos wat die waardes op die
  
                       horisontale tyd-as toeneem
  
                       sodat daar 'n styging in koste
  
                       is soos wat die tyd toeneem.
  
                                                                 [ V 10.3 ]
  
  
             10.4.1   R50,00                           [ V 10.4.1 ]
  
  
             10.4.2   150 minute                     [ V 10.4.2 ]
  
  
             10.4.3   R125,00                         [ V 10.4.3 ]
  
  
             10.4.4   350 minute                     [ V 10.4.4 ]
  
  
  
             10.1   The graph starts at the point
  
                       (0 ; 50). There is now a fixed
  
                       cost of R50 which does not
  
                       depend on the time.
  
                                                                 [ Q 10.1 ]
  
  
             10.2   From A to B the graph is
  
                       parallel to the horizontal
  
                       time-axis so that there is no
  
                       change in the value on the
  
                       vertical cost-axis although
  
                       the time increases,
  
                       i.e. from A to B the cost
  
                       remains constant on R50
  
                       although the time increases
  
                       from 0 to 100 minutes.
  
                                                                   [ Q 10.2 ]
  
  
             10.3   From B to C the graph slopes
  
                       upward so that the values on
  
                       the vertical cost-axis increase
  
                       as the values on the horizontal
  
                       time-axis increase causing an
  
                       increase in the cost as
  
                       the time increases.
  
                                                                 [ Q 10.3 ]
  
  
             10.4.1   R50,00                           [ Q 10.4.1 ]
  
  
             10.4.2   150 minutes                   [ Q 10.4.2 ]
  
  
             10.4.3   R125,00                         [ Q 10.4.3 ]
  
  
             10.4.4   350 minutes                   [ Q 10.4.4 ]
  
  
  
             10.5   Die vaste fooi van R50 moet afgetrek word van die R200 om die koste vir 300 minute te kry.
  
                       The fixed cost of R50 must be deducted from thr R200 to calculate the cost for 300 minutes.
  
  
                       Koste vir die minute gebruik / Cost for the minutes used = R200 - R50 = R150
  
  
                                                                                              R150
                       Koste per minuut / Cost per minute  = ————————  = R0,50
                                                                                      300 minute(s)                                                        [ V/Q 10.5 ]
  
  
  
             10.6   10.4.1  Koste / Cost  =  R50 + (0,40 x 100)    =  R(50 + 40)    =  R90,00
  
  
                       10.4.2  Koste vir minute gebruik / Cost for minutes used = R(80 - 50) = R30
  
                                                               R30
                                   Tyd / Time  =  ──────  = 60 minute(s)
                                                             R0,50
  
  
                       10.4.3  Koste / Cost  =  R50 + (0,50 x (250 - 100)) = R(50 + 75) = R125,00
  
  
                       10.4.4  Koste vir minute gebruik / Cost for minutes used = R(175 - 50) = R125
  
                                                               R125
                                   Tyd / Time  =  ──────  = 250 minute(s)
                                                             R0,50
  
  
                                   Tyd / Time  =  250 + 100 minute(s) = 350 minute(s)                                                [ V/Q 10.6 ]
  
  
Antwoorde  / Answers  11  
  
             11.1   Die grafiek begin nie by 0
  
                       nie, want daar is 'n vaste
  
                       koste van R50
  
                       onafhanklik van die tyd is.
  
                                                                 [ V 11.1 ]
  
  
             11.2   kontrak A R90
  
                       kontrak B R60                   [ V 11.2 ]
  
  
             11.3   kontrak A 375 minute
  
                       kontrak B 333.3 minute
                                                                 [ V 11.3 ]
  
  
             11.4   R is die punt (250 ; 150)
  
                                                                 [ V 11.4 ]
  
  
             11.1   The graph does not start at
  
                       0 because there is a fixed
  
                       cost of R50 which does not
  
                       depend on the time.
  
                                                                 [ Q 11.1 ]
  
  
             11.2   contract A R90
  
                       contract B R60                  [ Q 11.2 ]
  
  
             11.3   contract A 375 minutes
  
                       contract B 333,3 minutes
  
                                                                   [ Q 11.3 ]
  
  
             11.4   R is the point (250 ; 150)
  
                                                                   [ Q 11.4 ]
  
  
             11.5   By punt R is die koste R150 vir 250 minute.
  
                       At point R the cost is R150 for 250 minutes.
  
  
                                                                                              R150
                       Koste per minuut / Cost per minute  = ————————  = R0,60   = 60 c
                                                                                      250 minute(s)                                                        [ V/Q 10.5 ]
  
  
  
             11.6   By punt R is die koste R150 vir 250 minute.
  
                       At point R the cost is R150 for 250 minutes.
  
  
                       Die vaste fooi van R50 moet afgetrek word van die R150 om die koste vir 250 minute te kry.
  
                       The fixed cost of R50 must be deducted from thr R150 to calculate the cost for 250 minutes.
  
  
                       Koste vir die minute gebruik / Cost for the minutes used = R150 - R50 = R100
  
  
                                                                                              R100
                       Koste per minuut / Cost per minute  = ————————  = R0,40
                                                                                      250 minute(s)                                                        [ V/Q 11.6 ]
  
  
  
             11.7.1   Kontrak B omdat die koste vir 200 en minder minute op kontrak B minder is as die op
  
                          kontrak A. By 200 minute is die koste op kontrak B R120 terwyl dit op kontrak A R130 is.
  
                          Die koste is dus minder.                                                                                        [ V/Q 11.7.1 ]
  
  
  
                          Contract B because the cost for 200 minutes and less on contract B is less than that on
  
                          contract B. At 200 minutes the cost on contract B is R120 while on contract A it is R130.
  
                          The cost is thus smaller.                                                                                        [ V/Q 11.7.1 ]
  
  
  
             11.7.2   Kontrak A omdat die koste vir 260 en meer minute op kontrak A minder is as die op
  
                          kontrak B. By 260 minute is die koste op kontrak A R154 terwyl dit op kontrak B R156 is.
  
                          Die koste is dus minder.                                                                                        [ V/Q 11.7.2 ]
  
  
  
                          Contract A because the cost for 260 minutes and more on contract A is less than that on
  
                          contract B. At 260 minutes the cost on contract A is R154 while on contract B it is R156.
  
                          The cost is thus smaller.                                                                                        [ V/Q 11.7.2 ]
  
  
  
  
  
  
  
  
  
  
  
  
  
  FINIS FINIS FINIS ENDE ENDE ENDE EINDE EINDE EINDE END END END E FIDELE E FIDELE