John had 25% more stickers than Jack. Julie had 50% fewer stickers than John. John and Jack gave Julie some stickers in the ratio of 4 : 5. As a result, Julie had 60% more stickers than before. Given that Jack had 10 less stickers than Julie in the end, how many stickers did Jack give to Julie?

John	Jack	Julie
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

John : Jack = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

John : Julie = 2 : 1

The number of stickers that John had at first is repeated. Make the number of stickers that John had at first the same.  LCM of 5 and 2 is 10.

	John	Jack	Julie
Before	10x3 =  30 u	8x3 = 24 u	5x3 = 15 u
Change			+ 3x3 = + 9 u
Comparing the changes in the number of stickers	- 4x1 = - 4 u	- 5x1 = - 5 u	+ 9x1 = + 9 u
After	26 u	19 u	8x3 = 24 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of stickers that John and Jack gave to Julie is repeated.  Make the total number of stickers that John and Jack gave to Julie the same.  LCM of 9 and 3 is 9.

Number of stickers that Jack had less than Julie 
= 24 u - 19 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Number of stickers that Jack gave to Julie
= 5 u
= 5 x 2
= 10

Answer(s): 10