Sofia bought 50% more coins than Avery. Isabella bought 35% fewer coins than Sofia. Sofia and Avery gave Isabella some coins in the ratio 2 : 1. As a result, Isabella had twice as much coins as before. Given that Sofia had 24 less coins than Avery in the end, how much coins did Sofia and Avery give to Isabella?

	Sofia	Avery	Isabella
	3x20	2x20
	20x3		13x3
Before	60 u	40 u	39 u
Change			+ (2 x 39 u) = + 78 u
	- 2x26 = - 52 u	- 1x26 = - 26 u	+ 3x26 =  + 78 u
After	8 u	14 u	117 u

100% + 50% = 150%
150% = ¹⁵⁰₁₀₀ = ³₂

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of coins that Sofia had at first is the repeated identity.
LCM of 3 and 20 = 60

The change in the number of coins that Isabella had is the repeated identity when Sofia and Avery gave to Isabella.
LCM of 78 and 3 = 78

Number of coins that Sofia had less than Avery in the end
= 14 u - 8 u
= 6 u

6 u = 24
1 u = 24 ÷ 6 = 4

Number of coins that Sofia and Avery gave to Isabella
= 52 u + 26 u
= 78 u
= 78 x 4
= 312

Answer(s): 312