Tina, Raeann and Gem had a sum of money. The amount of money Tina had was ²₅ of the amount of money Raeann had. The ratio of the amount of money Raeann had to the total amount of money Gem and Raeann had was 3: 7. After Gem gave $35 to Raeann, she had as much money as Raeann. How much more money did Gem have than Tina in the end?

Tina	Raeann	Gem
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
6 u	15 u	20 u

The amount that Raeann had is the repeated identity. Make the amount that Raeann had the same.  LCM of 5 and 3 is 15.

	Tina	Raeann	Gem
Before	6 u	15 u	20 u
Change	No change	+ 35	- 35
After	6 u	15 u + 35	20 u - 35

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

20 u - 35 = 15 u + 35
20 u - 15 u = 35 + 35 
5 u = 70

1 u = 70 ÷ 5 = 14

Amount that Gem had more than Tina in the end
= 20 u - 35 - 6 u
= 14 u - 35
= 14 x 14 - 35
= 196 - 35
= $161

Answer(s): $161