Roy spent 3/8 of his money on 10 identical files and 10 identical board games.
He then spent 1/10 of the remainder on 6 identical staplers.
A board game cost 5 times as much as file. A stapler cost $1.50 more than a file.
(a) How much did Roy spend on a file?
(b) How much did Roy spend on a board game?
Let money with Roy = x.
Money spent on 10 identical files and 10 identical board games = 3/8x.
Money remaining = x - 3/8x = (8x - 3x)/8 = 5x/8
1/10 of remainder spent on 6 identical staplers
=> 1/10 * 5/8x = 1/16x
Money spent on 1 stapler = 1/16x / 6 = x/96
Let cost of file be y
then cost of board games = 5y
Cost of stapler = $1.5 + y = x/96
= 1194 + y = x
Also, money spent on 10 files and 10 board games =>
10y + 10(5y) = 3/8x = 10y + 50y = 3/8 (1194 + y) [By substitution x from (1)]
= 60y * 8 = 3 (1194 + y)
480y = 3582 + 3y
y = 3582/477 = $7.5
Money spent on 1 file = $7.5
Momey spent on board game = 5y
= 5 * 7.5 = $37.5
