Nora bought 25% more beads than Ethan. Anthony bought 20% fewer beads than Nora. Nora and Ethan gave Anthony some beads in the ratio 3 : 2. As a result, Anthony had twice as much beads as before. Given that Ethan had 12 more beads than Nora in the end, how much beads did Anthony receive?

	Nora	Ethan	Anthony
	5x5	4x5
	5x5		4x5
Before	25 u	20 u	20 u
Change			+ (2 x 20 u) = + 40 u
	- 3x8 = - 24 u	- 2x8 = - 16 u	+ 5x8 =  + 40 u
After	1 u	4 u	60 u

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

100% - 20% = 80%
80% = ⁸⁰₁₀₀ = ⁴₅

The number of beads that Nora had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of beads that Anthony had is the repeated identity when Nora and Ethan gave to Anthony.
LCM of 40 and 5 = 40

Number of beads that Ethan had more than Nora in the end
= 4 u - 1 u
= 3 u

3 u = 12
1 u = 12 ÷ 3 = 4

Number of beads that Anthony received
= 24 u + 16 u
= 40 u
= 40 x 4
= 160

Answer(s): 160