A store owner paid a total of $900 for some sweaters and some vests. He paid $540 less for the sweaters than the vests. Each vest cost $25 more than each sweater. The number of sweaters he bought was ²₃ of the number of vests bought.

1. How much did he pay for all the sweaters?
2. How many sweaters did he buy?

	Sweaters	Vests	Difference in cost	Number of items in 1 set
Number of sets	2	3
Total cost	$180	$720
Cost of 1 set	180 ÷ 2 = $90	720 ÷ 3 = $240	240 - 90 = $150
Cost of each item	1 u	1 u + $25	$25	150 ÷ 25 = 6

(a)
Total amount = $900
Total amount spent on sweaters = (900 - 540) ÷ 2 = $180
Total amount spent on vests = 180 + 540 = $720

Amount that he paid for all the sweaters = $180

(b)
2 sets of sweaters = $180
3 sets of vests = $720

1 set of sweaters = 180 ÷ 2 = $90
1 set of vests = 720 ÷ 3 = $240

Difference in the amount paid for each set of vests and sweaters
= 240 - 90
= $150

The extra $150 is due to each vest costing $25 more than each sweater.

Number of sweaters in 1 set
= 150 ÷ 25
= 6

Number of sweaters that he bought
= 2 sets of sweaters
= 2 x 6
= 12

Answer(s): (a) $180; (b) 12