Cody had $288 and Howard had $116 at first. Each of them bought an identical hoodie and an identical coat from the same shop. The coat cost 4 times as much as the hoodie. In the end, Cody had 3 times as much money as Howard. What was the cost of the hoodie?

	Cody	Howard	Difference
Before	$288	$116	$172
Change	- 1 hoodie - 1 coat	- 1 hoodie - 1 coat
After	3 u	1 u	2 u

Since Cody and Howard bought the same items, the difference  in their amounts remains the same.

Difference in the amounts that they had
= 3 u - 1 u
= 2 u

2 u = 288 - 116
2 u = 172

1 u = 172 ÷ 2 = 86

Amount that Howard had in the end
= 1 u
= $86

Cost of 1 hoodie and 1 coat
= 116 - 1 u
= 116 - 86
= $30

The coat cost 4 times as much as the hoodie.

Cost of 1 hoodie = 1 p
Cost of 1 coat = 4 p

Total cost of 1 hoodie and 1 coat
= 1 p + 4 p
= 5 p

5 p = 30

1 p = 30 ÷ 5 = 6

Cost of the hoodie
= 1 p
= $6

Answer(s): $6