Zoe, Gem and Rachel had a sum of money. The amount of money Zoe had was ²₅ of the amount of money Gem had. The ratio of the amount of money Gem had to the total amount of money Rachel and Gem had was 2: 7. After Rachel gave $15 to Gem, she had as much money as Gem. How much more money did Rachel have than Zoe in the end?

Zoe	Gem	Rachel
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	5x5 = 25 u
4 u	10 u	25 u

The amount that Gem had is the repeated identity. Make the amount that Gem had the same.  LCM of 5 and 2 is 10.

	Zoe	Gem	Rachel
Before	4 u	10 u	25 u
Change	No change	+ 15	- 15
After	4 u	10 u + 15	25 u - 15

The amount that Rachel and Gem had in the end is the same.

25 u - 15 = 10 u + 15
25 u - 10 u = 15 + 15 
15 u = 30

1 u = 30 ÷ 15 = 2

Amount that Rachel had more than Zoe in the end
= 25 u - 15 - 4 u
= 21 u - 15
= 21 x 2 - 15
= 42 - 15
= $27

Answer(s): $27