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

	Kaylee	Hazel	Aria
	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 marbles that Kaylee had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of marbles that Aria had is the repeated identity when Kaylee and Hazel gave to Aria.
LCM of 40 and 5 = 40

Number of marbles that Hazel had more than Kaylee in the end
= 4 u - 1 u
= 3 u

3 u = 18
1 u = 18 ÷ 3 = 6

Number of marbles that Aria received
= 24 u + 16 u
= 40 u
= 40 x 6
= 240

Answer(s): 240