In a shop, some jigsaw puzzles and toy rifles were on sale. ¹₅ of the items were jigsaw puzzles. ¹₃ of the jigsaw puzzles and 69 toy rifles were sold. There were ¹₆ of the items left in the shop. How many jigsaw puzzles and toy rifles were there in the shop at first?

	Jigsaw puzzles	Toy rifles	Total
Comparing jigsaw puzzles  and toy rifles at first	1x6 = 6 u	4x6 = 24 u	5x6 = 30 u
Before	3x2 =  6 u		6x5 = 30 u
Change	- 1x2 = - 2 u	- 69	- 5x5 = - 25 u
After	2x2 = 4 u	1 u	1x5 = 5 u

 
The total number of toys at first is repeated.  Make the total number of toys at first the same. LCM of 5 and 6 is 30.

The number of jigsaw puzzles at first is repeated.  Make the number of jigsaw puzzles the same. LCM of 6 and 3 is 6. 

Number of toy rifles left
= 5 u - 4 u
= 1 u

Number of toy rifles sold
= 24 u - 1 u
= 23 u

23 u = 69

1 u = 69 ÷ 23 = 3

Number of jigsaw puzzles and toy rifles at first
= 30 u
= 30 x 3
= 90

Answer(s): 90