Gwen's shop sold vests and coats. The vests were sold at $90 each and each coat was sold at ²₅ of the price of each vest. Gwen sold ¹₂ of the items on the first day and collected $11664. ⁵₆ of the items sold on the first day were vests.

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

(a)

Sold		Unsold	Total
1x6		1x6	2x6
Vests	Coats
5x1	1x1
5 u	1 u	6 u	12 u

The total number of vests and coats sold is repeated.  Make the total number of vests and coats sold the same.  LCM of 6 and 1 is 6.

	Vests	Coats	Total
Number	5 u	1 u	6 u
Value	$90	$36
Total value	450 u	36 u	486 u

Cost of each coat
= ²₅ x 90
= $36

Total amount collected from selling the vests and the coats on the first day
= 450 u + 36 u
= 486 u

486 u = 11664

1 u = 11664 ÷ 486 = 24

Number of coats sold on the first day
= 1 u
= 24

(b)
Total number of items left after the first day
= 6 u
= 6 x 24
= 144

Answer(s): (a) 24; (b) 144