Jacob bought 25% more buttons than John. Jayden bought 20% fewer buttons than Jacob. Jacob and John gave Jayden some buttons in the ratio 3 : 2. As a result, Jayden had twice as much buttons as before. Given that John had 24 more buttons than Jacob in the end, how much buttons did Jayden receive?

	Jacob	John	Jayden
	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 Jacob had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of buttons that Jayden had is the repeated identity when Jacob and John gave to Jayden.
LCM of 40 and 5 = 40

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

3 u = 24
1 u = 24 ÷ 3 = 8

Number of buttons that Jayden received
= 24 u + 16 u
= 40 u
= 40 x 8
= 320

Answer(s): 320