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

	Gabriel	Risa	Bryan
	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 buttons that Gabriel had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of buttons that Bryan had is the repeated identity when Gabriel and Risa gave to Bryan.
LCM of 40 and 5 = 40

Number of buttons that Risa had more than Gabriel in the end
= 4 u - 1 u
= 3 u

3 u = 12
1 u = 12 ÷ 3 = 4

Number of buttons that Bryan received
= 24 u + 16 u
= 40 u
= 40 x 4
= 160

Answer(s): 160