Antwoorde / Answers 1.
N.B. Die volgende afkortings word in die antwoorde, waar nodig, gebruik :
N.B. The following abbreviations are used, where necessary, in the answers :
KP / CP : kosprys / cost price
AD% : persentasie afslag /
percentage discount
JB/YP : jy betaal / you pay
P(R) : wins Rand / profit Rand
BTW / VAT
VP / SP : verkoopprys / selling price
AD(R) : afslag gegee / discount given
%P : persentasie wins / percentage profit
FP(R) : finale prys / final price
1.1 Afslag = Afslag % × Verkoopprys
a = AD% × VP / SP
10
a = R ──── × 115
100
= 11,50
Jy betaal = Verkoopprys −
Afslag gegee
b = VP − ADR
= R115 − R11,50
= R103,50
[ 1.1 ]
1.2 Afslag = Afslag % × Verkoopprys
5
c = R ─── × 218,15
100
= R 10,91
Jy betaal = Verkoopprys − afslag
d = R218,15 − R10,91
= R207,24
[ 1.2 ]
1.3 Persentasie Afslag
Afslag gegee 100
= ────────── × ───
Verkoopprys 1
4,10 100
e = ───── × ─── %
63 1
= 6,51 %
Jy betaal = Verkoopprys − Afslag
Afslag gegee = f = R 63 − R 4,10
= R58,90
[ 1.3 ]
1.4 Persentasie Afslag
Afslag gegee 100
= ────────── × ───
Verkoopprys 1
61,20 100
g = ───── × ─── %
816 1
= 7,5 %
Jy betaal = Verkoopprys − Afslag
Afslag gegee = R 816 − R 61,20
= R 816 − R 61,20
= R754,80
[ 1.4 ]
1.5 Afslag gegee
= Verkoopprys − Jy betaal
Jy betaal = k = R 794,00 − R 730,48
= R 63,52
Persentasie Afslag
Afslag gegee 100
= ────────── × ───
Verkoopprys 1
63,52 100
j = ───── × ─── %
794 1
= 8 %
[ 1.5 ]
1.6 Verkoopprys
= Jy betaal + Afslag gegee
m = R 353,17 + R 62,33
= R415,50
Persentasie Afslag
Afslag gegee 100
= ────────── × ───
Verkoopprys 1
62,33 100
n = ───── × ─── %
415,50 1
= 15,00
[ 1.6 ]
1.1 Discount = Discount % × Selling price
a = AD% × VP / SP
10
a = R ──── × 115
100
= 11,50
You pay = Selling price −
Discoount given
b = VP − ADR
= R115 − R11,50
= R103,50
[ 1.1 ]
1.2 Discount = Discount % × Selling price
5
c = R ─── × 218,15
100
= R 10,91
You pay = Seeling price − discount
d = R218,15 − R10,91
= R207,24
[ 1.2 ]
1.3 Percentage discount
Discount given 100
= ─────────── × ───
Selling price 1
4,10 100
e = ───── × ─── %
63 1
= 6,51 %
You pay = Selling price − Discount
Discount given = f = R 63 − R 4,10
= R58,90
[ 1.3 ]
1.4 Percentage discount
Discount given 100
= ────────── × ───
Selling price 1
61,20 100
g = ───── × ─── %
816 1
= 7,5 %
You pay = Selling price − discount
Afslag gegee = h = R 816 − R 61,20
= R 816 − R 61,20
= R754,80
[ 1.4 ]
1.5 Discount given
= Selling price − You pay
You pay = k = R 794,00 − R 730,48
= R 63,52
Percentage discount
Discount given 100
= ────────── × ───
Selling price 1
63,52 100
j = ───── × ─── %
794 1
= 8 %
[ 1.5 ]
1.6 Selling price
= You pay + Discount given
m = R 353,17 + R 62,33
= R415,50
Percentage discount
Discount given 100
= ─────────── × ───
Selling price 1
62,33 100
n = ───── × ─── %
415,50 1
= 15,00
[ 1.6 ]
2.1 Wins (R) / Profit (R)
= Persentasie wins/Percentage profit ×
Kosprys/Cost price
a = P% × KP/CP
8
= R ──── × 45,52
100
= R 3,64
Verkoopprys / Selling price
= Kosprys/Cost price + Wins/Profit
b = KP/CP + P(R)
= R45,52 + R 3,64
= R49,16 %
[ 2.1 ]
2.3 Persentasie wins / Percentage profit
Wins / Profit 100
= ─────────────── × ─── %
Koopprys / Cost price 1
P(R) 100
e = ────── × ─── %
KP/CP 1
16,25 100
e = ───── × ─── %
25 1
= 65,00 %
Verkoopprys / Selling price
= Kosprys/Cost price + Wins/Profit
f = R 25 + R 16,25
= R 41,25
[ 2.3 ]
2.5 Kosprys / Cost price
= Verkoopprys/Selling price −
Wins/Profit
k = VP/SP − P(R)
= R 742,03 − R 96,79
= R 645,24
Persentasie wins / Percentage profit
Wins / Profit 100
= ─────────────── × ─── %
Koopprys / Cost price 1
96,79 100
m = ───── × ─── %
645,24 1
= 15,00 %
[ 2.5 ]
2.7
As die wins % = 10% en die
koopprys = R100 is die wins R10 en
die verkoopprys = R110
As die PR% = 10% en die VP/SP = R110
is die P(R) = R10 en die KP/CP = R100
2.2 Wins (R) / Profit (R)
= Persentasie wins/Percentage profit ×
Kosprys/Cost price
c = P% × KP/CP
25
= R ──── × 25,80
100
= R 6,45
Verkoopprys / Selling price
= Kosprys / Cost price + Wins / Profit
d = KP/CP + P(R)
= R25,80 + R 6,45
= R32,25 %
[ 2.2]
2.4 Kosprys / Cost price
= Verkoopprys/Selling price − Wins/Profit
g = VP/SP − P(R)
= R 428,61 − R 107,07
= R 321,54
Persentasie wins/Percentage profit
Wins / Profit 100
= ─────────────── × ─── %
Koopprys / Cost price 1
107,07 100
h = ───── × ─── %
321,54 1
= 33,299 %
[ 2.4 ]
2.6 Wins / Profit
= Verkoopprys/Selling price −
Koopprys/Cost price
p = VP/SP − KP/CP
= R 25,08 − R 21,25
= R 3,83
Persentasie wins / Percentage profit
Wins / Profit 100
= ─────────────── × ─── %
Koopprys / Cost price 1
107,07 100
h = ───── × ─── %
321,54 1
= 33,299 %
[ 2.6 ]
2.7
If the profit % = 10% and the
Cost price = R100, the profit is R 110
and the selling price = R110
If the PR% = 10% and the VP/SP = R110,
the profit = R10 and the KP/CP = R100
∴ As die / If the PR% = 10% en die / and the VP/SP = R110 is die / the KP/CP = R100
en die / and the VP/SP = R110 en die / and the P(R) = R10
∴ As / If PR% = 8,5% en / and VP/SP = R108,50 is / KP/CP = R100 en / and P(R) = R8,50
100 8,50
∴ As / If PR% = 8,5% en / and VP/SP = R 1 is / KP/CP = R ────── en / and P(R) = R ──────
108,50 108,50
100
∴ As/If PR% = 8,5% en/and VP/SP = R 52,34 is KP/CP = R───── × 52,34 en/and
108,50
8,50
P(R) = R ────── × 52,34
108,50
∴ As die persentasie wins = 8,5% en die verkoopprys = R 52,34 is die koopprys = R 48,24 en
en die wins = R 4,10
∴ If the percentage profit = 8,5% and the Selling price = R 52,34 the Cost price = R 48,24
and the P(R) = R4,10
q = R48,24 ; r = R4,10
[ 2.7 ]
2.8
As die wins persentasie = 12,5% en
die koopprys = R100 is die wins
R12,50 en die verkoopprys = R112,50
As die persentasie wins = 12,50% en die
verkoopprys = R112,50 is die wins
R12,50 en die koopprys = R100
2.8
If the percentage profit = 12,50% and
the cost price = R100, the profit is
R 12,50 and the selling price = R112,50
If the percentage profit = 12,50% and the
Selling price = R 112,50, the profit is
R 12,50and the cost price = R 100
∴ As die persentasie wins = 10% en die Verkoopprys = R 110 is die Koopprys = R 100
en die wins = R 10
∴ If the percentage profit = 10% and the Selling price = R 110 the Cost price = R 100 and
and the profit = R 10
∴ As die persentasie wins = 12,5% en die Verkoopprys = R 112,50 is die Kosprys = R100 en
en die wins = R 12,50
∴ If the percentaage profit = 12,5% and the Selling price = R112,50 the Cost price = R100 and
and the profit = R 12,50
100 12,50
∴ As/If PR% = 12,5% en/and VP/SP = R 1 is /the KP/CP = R ──── en/and P(R) = R ─────
112,50 112,50
100
∴ As / If PR% = 12,5% en / and VP/SP = R 36,68 is die / the KP/CP = R ───── × 36,68
112,50
100
en die / and the P(R) = R ───── × 36,68
112,50
∴ As die persentasie wins = 12,5% en die Verkoopprys = R36,68 is die Kosprys = R32,60
en die wins = R4,08
∴ If the percentage profit = 12,5% and the Selling price = R36,68 the Cost price = R32,60
and the profit = R4,08
s = R32,60 ; t = R4,08
[ 2.8 ]
3.1 BTW / VAT =
15% van/of verkoopprys/selling price
BTW / VAT
= 15% × VP/SP
a = 15% × VP/SP
15
= ──── × R 15
100
= R 2,25
Finale prys / Final price
= Verkoopprys/Selling price + BTW/VAT
b = VP/SP + BTW / VAT
= R15 + R2,25
= R17,25
[ 3.1 ]
3.2 BTW / VAT =
15% van/of verkoopprys/selling price
BTW / VAT
= 15% × VP/SP
c = 15% × VP/SP
15
= ──── × R 36,25
100
= R 5,44
Finale prys / Final price
= Verkoopprys/Selling price + BTW/VAT
b = VP/SP + BTW / VAT
= R36,25 + R5,44
= R41,69
[ 3.2 ]
3.3
As die BTW % = 15% en die verkoopprys = R 100, is die BTW R 15 en die finale prys R 115,00 /
If the VAT % = 15% and the selling price = R 100, the VAT = R15,00 and the final price = R 115,00.
As die BTW % = 15% en die finale prys = R 115,00, is die verkoopprys = R 100,00 en die BTW = R 15
If the VAT % = 15% and the final price = R 115,00, the selling price = R 100,00 and the VAT = R 15.
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R115, is die/the VP/SP = R100
en die/and the BTW/VAT = R15
100
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R1, is die/the VP/SP = R ─────
115
15,0
en die/and the BTW/VAT = R ─────
115
100
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R135,48, is die/the
115
100 15,0
koopprys/cost price = R ──── × 135,48 en die/and the BTW/VAT = R ──── × 135,48
115 115
∴ As die / If the BTW/VAT% = 15% en die / and the FP(R) = R135,48 is die / the
Verkoopprys/Selling price = R117,81 en die / and the BTW/VAT = R17,67
OF / OR
100
15
Verkoopprys/Selling price = R ──── × 135,48 en die/and the BTW/VAT = R ──── × 135,48
115
115
Verkoopprys / Selling price = R 117,81 en die / and the BTW/VAT = R 17,67
e = R117,81 ; f = R17,67
[ 3.3 ]
3.4
As die BTW % = 15% en die verkoopprys = R100,00, is die BTW = R15,00 en die
finale prys R115,00 /
If the VAT % = 15% and the selling price = R 100, the VAT = R15,00 and the final price = R 115,00.
As die BTW % = 15% en die finale prys = R 115,00, is die verkoopprys = R 100,00 en die BTW = R 15
If the VAT % = 15% and the final price = R 115,00, the selling price = R 100,00 and the VAT = R 15.
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R115, is die/the VP/SP = R100
en die/and the BTW/VAT = R15
100
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R1, is die/the VP/SP = R ────
115
15,0
en die/and the BTW/VAT = R────
115
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R572,38, is die/the
100
15,0
verkoopprys/selling price = R ──── × 572,28 en die/and the BTW/VAT = R──── × 572,28
115
115
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R572,28 is die/the VP/SP = R117,81
en die / and the BTW / VAT = R17,67
g = R117,81 ; h = R17,67
[ 3.4 ]
3.5
BTW / VAT = 15% van / of verkoopprys / selling price
BTW / VAT
= 15% × Verkoopprys / Selling price
a = 15% × VP/SP
15
= ──── × R 804,51
100
= R 120,68
Finale prys / Final price
= Verkoopprys / Selling price + BTW / VAT
b = VP/SP + BTW / VAT
= R804,51 + R120,68
= R925,19
[ 3.5 ]
3.6
BTW / VAT = 15% van / of verkoopprys / selling price
BTW / VAT
= 15% × Verkoopprys / Selling price
a = 15% × VP/SP
15
= ──── × R55,64
100
= R8,35
Finale prys / Final price
= Verkoopprys / Selling price + BTW / VAT
b = VP/SP + BTW / VAT
= R55,64 + R8,35
= R63,99
[ 3.6 ]
3.7
As die BTW % = 15% en die verkoopprys = R100,00, is die BTW = R15,00 en die
finale prys R115,00 /
If the VAT % = 15% and the selling price = R 100, the VAT = R15,00 and the final price = R 115,00.
As die BTW % = 15% en die finale prys = R 115,00, is die verkoopprys = R 100,00 en die BTW = R 15
If the VAT % = 15% and the final price = R 115,00, the selling price = R 100,00 and the VAT = R 15.
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R115, is die/the VP/SP = R100
en die/and the BTW/VAT = R15
100
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R1, is die/the VP/SP = R ────
115
15,0
en die/and the BTW/VAT = R────
115
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R572,38, is die/the
100
15,0
verkoopprys/selling price = R ──── × 92,66 en die/and the BTW/VAT = R──── × 92,66
115
115
∴ As/If BTW/VAT% = 15% en/and finale prys/final price = R92,66 is die/the VP/SP = R80,57
en die / and the BTW / VAT = R12,09
p = R80,57 ; q = R12,09
[ 3.7 ]
4.1
Die koste van enige aantal kaartjies
is die produk van die aantal kaartjies
en die koste van een kaartjie.
c = 5n
[ 4.1 ]
4.2
Die inkomste van enige aantal kaartjies
is agt maal die aantal kaartjies verkoop.
a = 8q
[ 4.2 ]
4.3
Die wins is die inkomste van die aantal
kaartjies verkoop minus die koste om
om enige aantal kaartjies te koop.
P = a - c = 8q - 5n
[ 4.3 ]
4.4.1
q kan nie groter wees as n nie, want
jy kan nie meer kaartjies verkoop
as wat jy het nie.
[ 4.4.1 ]
4.4.2
As q = n is 8q > 5n, die inkomste
is groter as die uitgawe en jy
maak nog steeds 'n wins.
[ 4.4.2 ]
4.4.3
As q < n en 8q > 5n, maak jy
nog steeds 'n wins.
As q < n en 8q = 5n, breek jy
gelyk, die inkomste = die uitgawe
en wins = 0.
As q < n en 8q < 5n, maak jy
'n verlies, inkomste < uitgawe.
[ 4.4.3 ]
4.5
As die koste grpter is as
die inkomste, m.a.w. as 5n > 8q.
[ 4.5 ]
4.1
The cost of any number of picture cards
is the product of the number of cards
and the cost for one card.
c = 5n
[ 4.1 ]
4.2
The income from any number of
picture cards is eight eight times
the number of cards sold.
a = 8q
[ 4.2 ]
4.3
The profit is the income from the
cards sold minus the cost of any
number of picture cards bought.
P = a - c = 8q - 5n
[ 4.3 ]
4.4.1
q can not be greater than n,
because you cannot sell more cards
than you bought.
[ 4.4.1 ]
4.4.2
If q = n then 8q > 5n, the income
is greater than the expenses and
you still make a profit.
[ 4.4.2 ]
4.4.3
If q < n and 8q > 5n, you still make a
profit.
If q < n and 8q = 5n, you break even,
the income = the expenses and
the profit = 0.
If q < n and 8q < 5n, you make a
loss, the income < the expenses.
[ 4.4.3 ]
4.5
If the cost is greater than
the incomste, e.g. if 5n > 8q.
[ 4.5 ]
5.1
Wins per kaartje
= verkoopprys − aankoopprys
= R5,00 − R2,50
= R2,50
[ 5.1 ]
5.2
Persentasie wins
wins 100
= ───── × ──── %
koste 1
2,50 100
= ───── × ──── %
2,50 1
= 100 %
[ 5.2 ]
5.3 Inkomste = R4 500
, wins per kaartjie = R2,50
en n kaartjies moet per maand
verkoop word.
R2,50 × n = R4 500
4 500
n = ─────
2,50
= 1 800
[ 5.3 ]
5.4
Nuwe koste = ou koste + 18% R2,50
18
= R2,50 + ─── × R2,50
100
= R2,95
OF
Nuwe koste = 118% van die ou koste
118
= R2,50 × ────
100
= R2,95
Nuwe wins = R5,00 − R2,95 = R2,05
wins 100
Persentasie wins = ───── × ──── %
koste 1
2,05 100
= ──── × ─── %
2,95 1
= 69,4 %
[ 5.4 ]
5.5
R2,05 × n = R4 500
4 500
n = ─────
2,05
= 2 196
[ 5.5 ]
5.6
Jy wil weer 100& wins maak. Jy
moet dus 'n wins maak wat gelyk
is aan die produksiekoste, wat
nou R2,95 per kaartjie is.
Verkoopprys = R2,95 + R2,95
= R5,90
[ 5.6 ]
5.1
Profit per card = selling price − cost price
= R5,00 − R2,50
= R2,50
[ 5.1 ]
5.2
Percentage profit
profit 100
= ───── × ──── %
cost 1
2,50 100
= ───── × ──── %
2,50 1
= 100 %
[ 5.2 ]
5.3
Income = R4 500,
profit per card = R2,50
and n cards must be sold
per month.
R2,50 × n = R4 500
4 500
n = ─────
2,50
= 1 800
[ 5.3 ]
5.4
New cost = old cost + 18% of R2,50
18
= R2,50 + ─── × R2,50
100
= R2,95
OR
New cost = 118% of the old cost
118
= R2,50 × ────
100
= R2,95
New profit = R5,00 − R2,95 = R2,05
profit 100
Percentage profit = ───── × ─── %
cost 1
2,05 100
= ───── × ─── %
2,95 1
= 69,4 %
[ 5.4 ]
5.5
R2,05 × n = R4 500
4 500
n = ─────
2,05
= 2 196
[ 5.5 ]
5.6
You again want to make a profit of
100%. Therefore you have to make
a profit which is eqal to the production
cost, which is now R2,95 per card.
Selling price = R2,95 + R2,95
= R5,90
[ 5.6 ]
6.1
As die wins% = 15% en die finale prys = R 115,00, is die wins = R 15
If the profit % = 15% and the final price = R 115,00, the profit = R 15.
∴ As/If Wins%/profit% = 15% en/and finale prys/final price = R115, is die/the wins/profit = R15
15
∴ As/If Wins%/profit% = 15% en/and finale prys/final price = R1, is die/the wins/profit = R ────
115
15
∴ As/If Wins%/profit% = 15% en/and FP/FP = R2500, is die/the wins/profit = R ──── × 2500
115
d.i. / i.e. = R326,09
OF / OR
15
Wins / Profit = R ───
X 2 500 = R326.09
115
[ 6.1 ]
6.2
As die Wins % = 15% en die finale prys = R 115,00, is die kosprys = R 100,00
If the profit % = 15% and the final price = R 115,00, the cost price = R 100,00
∴ As/If Wins%/profit% = 15% en/and finale prys/final price = R115, is die/the KP/CP = R100
100
∴ As/If Wins%/profit%% = 15% en/and finale prys/final price = R1, is die/the KP/CP = R─────
115
100
∴ As/If Wins%/profit%% = 15% en/and FP/FP = R2500, is die/the KP/CP = R───── × 2500
115
d.i. / i.e. = R2 173,91
OF / OR
100
Kosprys / Cost price = R ───
X 2 500 = R2 173,91
115
OF / OR
Kosprys / Cost price = Verkoopprys / Selling price ━ Wins / Profit
= R 2 500 ━ R 326,09
= R 2 173,91
[ 6.2 ]
6.3
BTW / VAT = 15 % van / of Verkoopprys / Selling price
15
= R ───── × 2 500
100
= R 375
Koper betaal / Buyer pays = Verkoopprys / Selling price + BTW / VAT
= R 2 500 + R 375
= R 2 875
[ 6.3 ]
7.1
Wins / Profit = Verkoopprys / Selling price ━ Kosprys / Cost price
= R 2 100 ━ R 1 800
= R 300
[ 7.1 ]
7.2
wins / profit 100
Persentasie wins / Percentage profit = ──────────────
X ────
Kosprys / Cost Price 1
300 100
= ─────
X ────
1 800 1
= 16,667 %
[ 7.2 ]
8.1
As die verkoopprys + BTW = R115 is die BTW = R 15 en die verkoopprys = R 100
If the selling price + VAT = R115 the VAT = R 15 and the selling price = R 100
∴ As/If VP + BTW / SP + VAT = R115 is/the BTW/VAT R15 en/and VP/SP = R 100
15
100
∴ As/If VP + BTW / SP + VAT = R1 is/the BTW/VAT R ─── en/and VP/SP = R ────
115
115
15
∴ As/If VP + BTW / SP + VAT = R1 is/the BTW/VAT = R ────
X 4 299
115
= R 42,99
[ 8.1 ]
OF / OR
15
BTW / VAT = R ────
X 4 299
115
= R 42,99
[ 8.1 ]
8.2
100
∴ As/If VP + BTW / SP + VAT = R4 299 is/the VP/SP = R ────
X 4 299
115
= R 3 738,26
[ 8.2 ]
OF / OR
100
Verkoopprys / Selling price = R ────
X 4 299
115
= R 3 738,26
[ 8.2 ]
8.3
As die wins % = 25 % en die verkoopprys = R 125 is die kosprys = R 100
If the profit % = 25 % and the selling price = R 125 the cost price = R100
∴ As/If wins %/profit % = 25 % en die/and the VP/SP = R125 is die / the kosprys/cost price = R 100
100
∴ As/If wins %/profit % = 25 % en/and VP/SP = R1 is/the KP/CP = R ───
125
100
∴ As/If wins %/profit % = 25 % en/and VP/SP = R3 738,26 is/the KP/CP = R ───
X 3 738,26
125
= R 2 990,61
OF / OR
100
Kosprys / Cost price = R ────
X 3 738,26
125
= R 2 990,61
[ 8.3 ]