The exchange rate for the Australian dollar in January 2000 was AU$100 = S$x. In June 2000, the exchange rate had become AU$100 = S$(x-5). Karen found out that she could get an extra AU$32 for every S$672 that she exchanged in June compares to January. Form an equation in x and solve it.

Answer 1

January:
100 AU = x S
1 S = (100/x) AU ---> 672 S = (67200/x) AU

June:
100 AU = (x-5) S
1 S = (100/(x-5)) AU --- > 672 S = (67200/(x-5)) AU

67200/(x-5) AU - 67200/x AU = 32 AU
divide by AU, multiply by x(x-5)

67200x - 67200x + 336000 = 32x^2 - 160x
32x^2 - 160x - 336000 = 0
x^2 - 5x - 10500 = 0
(x-105)(x+100) = 0
x = 105 or x = -100 , but x > 0

so x = 105

so in Jan: AU$ 100 = S$ 105
in June : AU$ 100 = S$ 100

Answer 2

67200/(x-5) -

67200/ x AU=32AU