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

	Rael	David	Sophia
	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 cards that Rael had at first is the repeated identity.
LCM of 8 and 5 = 40

The change in the number of cards that Sophia had is the repeated identity when Rael and David gave to Sophia.
LCM of 48 and 3 = 48


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

1 u = 20

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

Answer(s): 340