Archie had $231 and Brandon had $101 at first. Each of them bought an identical cardigan and an identical sweater from the same shop. The sweater cost 3 times as much as the cardigan. In the end, Archie had 3 times as much money as Brandon. What was the cost of the cardigan?

	Archie	Brandon	Difference
Before	$231	$101	$130
Change	- 1 cardigan - 1 sweater	- 1 cardigan - 1 sweater
After	3 u	1 u	2 u

Since Archie and Brandon 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 = 231 - 101
2 u = 130

1 u = 130 ÷ 2 = 65

Amount that Brandon had in the end
= 1 u
= $65

Cost of 1 cardigan and 1 sweater
= 101 - 1 u
= 101 - 65
= $36

The sweater cost 3 times as much as the cardigan.

Cost of 1 cardigan = 1 p
Cost of 1 sweater = 3 p

Total cost of 1 cardigan and 1 sweater
= 1 p + 3 p
= 4 p

4 p = 36

1 p = 36 ÷ 4 = 9

Cost of the cardigan
= 1 p
= $9

Answer(s): $9