In a kiosk, some jigsaw puzzles and water guns were on sale. ¹₄ of the items were jigsaw puzzles. ²₃ of the jigsaw puzzles and 78 water guns were sold. There were ¹₉ of the items left in the kiosk. How many jigsaw puzzles and water guns were there in the kiosk at first?

	Jigsaw puzzles	Water guns	Total
Comparing jigsaw puzzles  and water guns at first	1x9 = 9 u	3x9 = 27 u	4x9 = 36 u
Before	3x3 =  9 u		9x4 = 36 u
Change	- 2x3 = - 6 u	- 78	- 8x4 = - 32 u
After	1x3 = 3 u	1 u	1x4 = 4 u

 
The total number of toys at first is repeated.  Make the total number of toys at first the same. LCM of 4 and 9 is 36.

The number of jigsaw puzzles at first is repeated.  Make the number of jigsaw puzzles the same. LCM of 9 and 3 is 9. 

Number of water guns left
= 4 u - 3 u
= 1 u

Number of water guns sold
= 27 u - 1 u
= 26 u

26 u = 78

1 u = 78 ÷ 26 = 3

Number of jigsaw puzzles and water guns at first
= 36 u
= 36 x 3
= 108

Answer(s): 108