Abigail bought 60% more hair clips than Joshua. Emily bought 40% fewer hair clips than Abigail. Abigail and Joshua gave Emily some hair clips in the ratio 2 : 1. As a result, Emily had twice as much hair clips as before. Given that Abigail had 20 less hair clips than Joshua in the end, how much hair clips did Abigail and Joshua have in the end?

	Abigail	Joshua	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 buttons that Abigail had at first is the repeated identity.
LCM of 8 and 5 = 40

The change in the number of buttons that Emily had is the repeated identity when Abigail and Joshua gave to Emily.
LCM of 48 and 3 = 48


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

1 u = 20

Number of hair clips that Abigail and Joshua had in the end
= 8 u + 9 u
= 17 u
= 17 x 20
= 340

Answer(s): 340