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

	Rebecca	Harper	John
	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 coins that Rebecca had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of coins that John had is the repeated identity when Rebecca and Harper gave to John.
LCM of 40 and 5 = 40

Number of coins that Harper had more than Rebecca in the end
= 4 u - 1 u
= 3 u

3 u = 18
1 u = 18 ÷ 3 = 6

Number of coins that John received
= 24 u + 16 u
= 40 u
= 40 x 6
= 240

Answer(s): 240