David spent 4/15 of his money on a pair of jeans. He paid $80 more
for a watch than for the pair of jeans. The remaining $130 was used to
buy a mini-compact disc player.
(a) What was the ratio of the amount of money spent on the watch to
the amount of money spent on the pair of jeans?
(b) What was David's original sum of money?
Let x be the amount of money David has.
Amount of money spent by David on a pair of jeans = 4/15x
Amount of money spent on watch = 4/15x + 80
4/15x + (4/15x + 80) + 130 = x
8/15x + 210 = x
=> 210 = x - 8/15x => 210 = 7x/15
x = $410 (Total amount of money David has initially)
(a) So, ratio of amount of money spent on the watch to the amount of money spent on pair of jeans.
= (4/15) (450) + 80)/ 4/15(450) = (120 + 80)/ 120
= 200/120 = 5/3 or 5:3
(b) David's required sum of money is x, which is $450