Wyatt bought 25% more beads than Julie. Joshua bought 20% fewer beads than Wyatt. Wyatt and Julie gave Joshua some beads in the ratio 3 : 2. As a result, Joshua had twice as much beads as before. Given that Julie had 30 more beads than Wyatt in the end, how much beads did Joshua receive?

	Wyatt	Julie	Joshua
	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 Wyatt had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of beads that Joshua had is the repeated identity when Wyatt and Julie gave to Joshua.
LCM of 40 and 5 = 40

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

3 u = 30
1 u = 30 ÷ 3 = 10

Number of beads that Joshua received
= 24 u + 16 u
= 40 u
= 40 x 10
= 400

Answer(s): 400