Julie bought 60% more hair clips than Elijah. Emily bought 40% fewer hair clips than Julie. Julie and Elijah gave Emily some hair clips in the ratio 2 : 1. As a result, Emily had twice as much hair clips as before. Given that Julie had 12 less hair clips than Elijah in the end, how much hair clips did Julie and Elijah have in the end?

	Julie	Elijah	Emily
	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 marbles that Julie had at first is the repeated identity.
LCM of 8 and 5 = 40

The change in the number of marbles that Emily had is the repeated identity when Julie and Elijah gave to Emily.
LCM of 48 and 3 = 48


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

1 u = 12

Number of hair clips that Julie and Elijah had in the end
= 8 u + 9 u
= 17 u
= 17 x 12
= 204

Answer(s): 204