Archie had $244 and Jack had $130 at first. Each of them bought an identical sweater and an identical jacket from the same shop. The jacket cost 3 times as much as the sweater. In the end, Archie had 4 times as much money as Jack. What was the cost of the sweater?

	Archie	Jack	Difference
Before	$244	$130	$114
Change	- 1 sweater - 1 jacket	- 1 sweater - 1 jacket
After	4 u	1 u	3 u

Since Archie and Jack bought the same items, the difference  in their amounts remains the same.

Difference in the amounts that they had
= 4 u - 1 u
= 3 u

3 u = 244 - 130
3 u = 114

1 u = 114 ÷ 3 = 38

Amount that Jack had in the end
= 1 u
= $38

Cost of 1 sweater and 1 jacket
= 130 - 1 u
= 130 - 38
= $92

The jacket cost 3 times as much as the sweater.

Cost of 1 sweater = 1 p
Cost of 1 jacket = 3 p

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

4 p = 92

1 p = 92 ÷ 4 = 23

Cost of the sweater
= 1 p
= $23

Answer(s): $23