Tim and Brandon had $180 and $123 respectively. Each of them bought a sweater and a cardigan at the same price. The cost of the sweater was 3 times as much as the cardigan. In the end, Tim had 4 times as much money as Brandon. What was the difference between the cost of the cardigan and the sweater?

	Tim	Brandon	Difference
Before	$180	$123	$57
Change	- 4 p	- 4 p
After	4 u	1 u	3 u

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

4 u - 1 u = 180 - 123
3 u = 57

1 u = 57 ÷ 3 = 19

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

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

4 p = 123 - 19
4 p = 104

1 p = 104 ÷ 4 = 26

Difference in the cost between the sweater and the cardigan
= 3 p - 1 p
= 2 p
= 2 x 26
= $52

Answer(s): $52