Julian had 50% more stickers than Caleb. Aubrey had 20% fewer stickers than Julian. Julian and Caleb gave Aubrey some stickers in the ratio of 1 : 3. As a result, Aubrey had 50% more stickers than before. Given that Caleb had 225 less stickers than Aubrey in the end, how many stickers did Caleb give to Aubrey?

Julian	Caleb	Aubrey
3x5	2x5
5x3		4x3
15	10	12

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

Julian : Caleb = 3 : 2

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

Julian : Aubrey = 5 : 4

The number of stickers that Julian had at first is repeated. Make the number of stickers that Julian had at first the same.  LCM of 3 and 5 is 15.

	Julian	Caleb	Aubrey
Before	15x2 =  30 u	10x2 = 20 u	12x2 = 24 u
Change			+ 6x2 = + 12 u
Comparing the changes in the number of stickers	- 1x3 = - 3 u	- 3x3 = - 9 u	+ 4x3 = + 12 u
After	27 u	11 u	18x2 = 36 u

50% x 12 
= ⁵⁰₁₀₀ x 12 
= 6 

The total number of stickers that Julian and Caleb gave to Aubrey is repeated.  Make the total number of stickers that Julian and Caleb gave to Aubrey the same.  LCM of 4 and 6 is 12.

Number of stickers that Caleb had less than Aubrey 
= 36 u - 11 u
= 25 u

25 u = 225

1 u = 225 ÷ 25 = 9

Number of stickers that Caleb gave to Aubrey
= 9 u
= 9 x 9
= 81

Answer(s): 81