Lilian bought 25% more coins than Jeremiah. Gavin bought 20% fewer coins than Lilian. Lilian and Jeremiah gave Gavin some coins in the ratio 3 : 2. As a result, Gavin had twice as much coins as before. Given that Jeremiah had 6 more coins than Lilian in the end, how much coins did Gavin receive?

	Lilian	Jeremiah	Gavin
	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 coins that Lilian had at first is the repeated identity.
LCM of 5 and 5 = 25

The change in the number of coins that Gavin had is the repeated identity when Lilian and Jeremiah gave to Gavin.
LCM of 40 and 5 = 40

Number of coins that Jeremiah had more than Lilian in the end
= 4 u - 1 u
= 3 u

3 u = 6
1 u = 6 ÷ 3 = 2

Number of coins that Gavin received
= 24 u + 16 u
= 40 u
= 40 x 2
= 80

Answer(s): 80