Christopher bought 60% more hair clips than Isaiah. Nora bought 40% fewer hair clips than Christopher. Christopher and Isaiah gave Nora some hair clips in the ratio 2 : 1. As a result, Nora had twice as much hair clips as before. Given that Christopher had 23 less hair clips than Isaiah in the end, how much hair clips did Christopher and Isaiah have in the end?

	Christopher	Isaiah	Nora
	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 erasers that Christopher had at first is the repeated identity.
LCM of 8 and 5 = 40

The change in the number of erasers that Nora had is the repeated identity when Christopher and Isaiah gave to Nora.
LCM of 48 and 3 = 48


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

1 u = 23

Number of hair clips that Christopher and Isaiah had in the end
= 8 u + 9 u
= 17 u
= 17 x 23
= 391

Answer(s): 391