Gary spent 5/8 of his money on 6 identical notebooks and 8 identical files. Each file cost thrice as much as each notebook. Then, he spent 4/9 of his remaining money on a magazine. The magazine cost $16.80 more than each notebook.

Question

(a) What fraction of Gary’s money was spent on the magazine? Give your answer in the simplest form.

(b) How much money had Gary left?

Answer 1

cost of notebook --- x
cost of file = 3x
cost of magazine = x + 16.8
total of Gary's money ----- m

6x + 8(3x) = (5/8)m
30x = 5m/8
240x = 5m
m = 48x

money remaining = 3/8 m
(4/9)(3/8)m = x + 16.8
(1/6)m = x + 16.8
m = 6x + 100.8

48x = 6x + 100.8
x = 2.4
and m = 48(2.4) = 115.20

then each notebook costs $2.40
each file costs $7.20
and the magazine costs $19.20

So you know that he had $115.20

Calculate how much he spent, and subtract that from 115.20