Aaron bought 50% more stickers than Raeann. Joseph bought 35% fewer stickers than Aaron. Aaron and Raeann gave Joseph some stickers in the ratio 2 : 1. As a result, Joseph had twice as much stickers as before. Given that Aaron had 18 less stickers than Raeann in the end, how much stickers did Aaron and Raeann give to Joseph?

	Aaron	Raeann	Joseph
	3x20	2x20
	20x3		13x3
Before	60 u	40 u	39 u
Change			+ (2 x 39 u) = + 78 u
	- 2x26 = - 52 u	- 1x26 = - 26 u	+ 3x26 =  + 78 u
After	8 u	14 u	117 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of stickers that Aaron had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of stickers that Joseph had is the repeated identity when Aaron and Raeann gave to Joseph.
LCM of 78 and 3 = 78

Number of stickers that Aaron had less than Raeann in the end
= 14 u - 8 u
= 6 u

6 u = 18
1 u = 18 ÷ 6 = 3

Number of stickers that Aaron and Raeann gave to Joseph
= 52 u + 26 u
= 78 u
= 78 x 3
= 234

Answer(s): 234