Riordan bought 60% more hair clips than Grace. Ava bought 40% fewer hair clips than Riordan. Riordan and Grace gave Ava some hair clips in the ratio 2 : 1. As a result, Ava had twice as much hair clips as before. Given that Riordan had 18 less hair clips than Grace in the end, how much hair clips did Riordan and Grace have in the end?

	Riordan	Grace	Ava
	8x5	5x5
	5x8		3x8
Before	40 u	25 u	24 u
Change			+ (2 x 24 u) = + 48 u
	- 2x16 = - 32 u	- 1x16 = - 16 u	+ 3x16 =  + 48 u
After	8 u	9 u	72 u

100% + 60% = 160%
160% = ¹⁶⁰₁₀₀ = ⁸₅

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of coins that Riordan had at first is the repeated identity.
LCM of 8 and 5 = 40

The change in the number of coins that Ava had is the repeated identity when Riordan and Grace gave to Ava.
LCM of 48 and 3 = 48


Number of hair clips that Riordan had less than Grace in the end
= 9 u - 8 u
= 1 u

1 u = 18

Number of hair clips that Riordan and Grace had in the end
= 8 u + 9 u
= 17 u
= 17 x 18
= 306

Answer(s): 306