Risa bought 25% more beads than Jayden. Abigail bought 20% fewer beads than Risa. Risa and Jayden gave Abigail some beads in the ratio 3 : 2. As a result, Abigail had twice as much beads as before. Given that Jayden had 21 more beads than Risa in the end, how much beads did Abigail receive?

	Risa	Jayden	Abigail
	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 Risa had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of beads that Abigail had is the repeated identity when Risa and Jayden gave to Abigail.
LCM of 40 and 5 = 40

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

3 u = 21
1 u = 21 ÷ 3 = 7

Number of beads that Abigail received
= 24 u + 16 u
= 40 u
= 40 x 7
= 280

Answer(s): 280