Liam and Ethan had $180 and $164 respectively. Each of them bought a shirt and a sweater at the same price. The cost of the shirt was 5 times as much as the sweater. In the end, Liam had 3 times as much money as Ethan. What was the difference between the cost of the sweater and the shirt?

	Liam	Ethan	Difference
Before	$180	$164	$16
Change	- 6 p	- 6 p
After	3 u	1 u	2 u

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

3 u - 1 u = 180 - 164
2 u = 16

1 u = 16 ÷ 2 = 8

Cost of 1 shirt = 5 p
Cost of 1 sweater = 1 p

Total cost of 1 shirt and 1 sweater
= 5 p + 1 p
= 6 p

6 p = 164 - 8
6 p = 156

1 p = 156 ÷ 6 = 26

Difference in the cost between the shirt and the sweater
= 5 p - 1 p
= 4 p
= 4 x 26
= $104

Answer(s): $104