Noah bought 25% more erasers than Maya. Luke bought 20% fewer erasers than Noah. Noah and Maya gave Luke some erasers in the ratio 3 : 2. As a result, Luke had twice as much erasers as before. Given that Maya had 18 more erasers than Noah in the end, how much erasers did Luke receive?

	Noah	Maya	Luke
	5x5	4x5
	5x5		4x5
Before	25 u	20 u	20 u
Change			+ (2 x 20 u) = + 40 u
	- 3x8 = - 24 u	- 2x8 = - 16 u	+ 5x8 =  + 40 u
After	1 u	4 u	60 u

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

The number of erasers that Noah had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of erasers that Luke had is the repeated identity when Noah and Maya gave to Luke.
LCM of 40 and 5 = 40

Number of erasers that Maya had more than Noah in the end
= 4 u - 1 u
= 3 u

3 u = 18
1 u = 18 ÷ 3 = 6

Number of erasers that Luke received
= 24 u + 16 u
= 40 u
= 40 x 6
= 240

Answer(s): 240