Answer:
(a) A = 0.00278787878787878x
(b) B = 0.00235294117647058x + 3
(c) The answers are as follows:
<u>For buying by credit card</u>
For 700 BWP: Cost = A = £1.95
For 800 BWP: Cost = A = £2.23
For 800 BWP: Cost = A = £2.79
<u>For buying from a Bureau de Change</u>
The equation (4) is used as follows:
For 700 BWP: Cost = B = £4.65
For 800 BWP: Cost = B = $4.88
For 1000 BWP: Cost = B = £5.35
(d) You would have to buy 6,897.54 pulas for the cost to be the same whether you use a credit card or cash.
Step-by-step explanation:
(a) by credit card
For the exchange rate, we have:
8.25 BWP = £1 ⇒ 8.25 / 8.25 BWP = £1 / 8.25 = 1.00 BWP = £0.121212121212121
The expression can therefore be written as follows:
A = £0.121212121212121 * r * x ................. (1)
Where;
A = cost (including commission) of buying a particular number of Botswana pulas by credit card
r = commission on a credit card transaction = 2.3%, or 0.023
x = the number of pulas bought
Substituting for r into equation (1), we have:
A = £0.121212121212121 * 0.023 * x
A = 0.00278787878787878x ................. (2)
Equation (2) is the expression.
(b) from a Bureau de Change
For the exchange rate, we have
8.5 BWP = £1 ⇒ 8.5 / 8.5 BWP = £1 / 8.5 = 1.00 BWP = 0.117647058823529
B = (£0.117647058823529 * r * x) + F ................. (3)
Where;
B = cost (including commission) of buying a particular number of Botswana pulas by from a Bureau de Change.
r = commission charged by Bureau de Change. = 2%, or 0.02
x = the number of pulas bought
F = fee = £3
Substituting for r and F into equation (3), we have:
B = (£0.117647058823529 * 0.02 * x) + £3
B = 0.00235294117647058x + 3 ................. (4)
Equation (4) is the expression.
c. Evaluate each of these expressions for 700 BWP, 800 BWP, and 1000 BWP respectively.
<u>For buying by credit card</u>
The equation (2) is used as follows:
For 700 BWP: A = £0.00278787878787878 * 700 = £1.95
For 800 BWP: A = £0.00278787878787878 * 800 = £2.23
For 800 BWP: A = £0.00278787878787878 * 1000 = £2.79
<u>For buying from a Bureau de Change</u>
The equation (4) is used as follows:
For 700 BWP: B = (£0.00235294117647058 * 700) + £3 = £1.65 + £3 = £4.65
For 800 BWP: B = (£0.00235294117647058 * 800) + £3 = £1.88 + £3 = $4.88
For 1000 BWP: B = (£0.00235294117647058 * 1000) + £3 = £2.35 + £3 = £5.35
d. Hazard a guess as to the number of pulas you would have to buy for the cost to be the same whether you use a credit card or cash.
This can be calculated by equating equations (2) and (4) and then solve for x as follows:
0.00278787878787878x = 0.00235294117647058x + 3
0.00278787878787878x - 0.00235294117647058x = 3
x(0.00278787878787878 - 0.00235294117647058) = 3
x0.0004349376114082 = 3
x = 3 / 0.0004349376114082
x = 6,897.54 pulas
Therefore, you would have to buy 6,897.54 pulas for the cost to be the same whether you use a credit card or cash.
. The first thing to do is to move the 
over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this: 
. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.