Dylan and Howard had $160 and $128 respectively. Each of them bought a cardigan and a sweater at the same price. The cost of the cardigan was 4 times as much as the sweater. In the end, Dylan had 5 times as much money as Howard. What was the difference between the cost of the sweater and the cardigan?

	Dylan	Howard	Difference
Before	$160	$128	$32
Change	- 5 p	- 5 p
After	5 u	1 u	4 u

Since Dylan and Howard bought the same items at the same price, the difference in the amounts they had remains unchanged at first and in the end.

5 u - 1 u = 160 - 128
4 u = 32

1 u = 32 ÷ 4 = 8

Cost of 1 cardigan = 4 p
Cost of 1 sweater = 1 p

Total cost of 1 cardigan and 1 sweater
= 4 p + 1 p
= 5 p

5 p = 128 - 8
5 p = 120

1 p = 120 ÷ 5 = 24

Difference in the cost between the cardigan and the sweater
= 4 p - 1 p
= 3 p
= 3 x 24
= $72

Answer(s): $72