Opal's shop sold windbreakers and sweaters. The windbreakers were sold at $40 each and each sweater was sold at ¹₂ of the price of each windbreaker. Opal sold ¹₂ of the items on the first day and collected $1380. ¹₂ of the items sold on the first day were windbreakers.

1. How many sweaters were sold on the first day?
2. What was the total number of items left after the first day?

(a)

Sold		Unsold	Total
1x2		1x2	2x2
Windbreakers	Sweaters
1x1	1x1
1 u	1 u	2 u	4 u

The total number of windbreakers and sweaters sold is repeated.  Make the total number of windbreakers and sweaters sold the same.  LCM of 2 and 1 is 2.

	Windbreakers	Sweaters	Total
Number	1 u	1 u	2 u
Value	$40	$20
Total value	40 u	20 u	60 u

Cost of each sweater
= ¹₂ x 40
= $20

Total amount collected from selling the windbreakers and the sweaters on the first day
= 40 u + 20 u
= 60 u

60 u = 1380

1 u = 1380 ÷ 60 = 23

Number of sweaters sold on the first day
= 1 u
= 23

(b)
Total number of items left after the first day
= 2 u
= 2 x 23
= 46

Answer(s): (a) 23; (b) 46