Gem, Elyse and Julie had a sum of money. The amount of money Gem had was ²₅ of the amount of money Elyse had. The ratio of the amount of money Elyse had to the total amount of money Julie and Elyse had was 4: 9. After Julie gave $70 to Elyse, she had as much money as Elyse. How much more money did Julie have than Gem in the end?

Gem	Elyse	Julie
2x4 = 8 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
8 u	20 u	25 u

The amount that Elyse had is the repeated identity. Make the amount that Elyse had the same.  LCM of 5 and 4 is 20.

	Gem	Elyse	Julie
Before	8 u	20 u	25 u
Change	No change	+ 70	- 70
After	8 u	20 u + 70	25 u - 70

The amount that Julie and Elyse had in the end is the same.

25 u - 70 = 20 u + 70
25 u - 20 u = 70 + 70 
5 u = 140

1 u = 140 ÷ 5 = 28

Amount that Julie had more than Gem in the end
= 25 u - 70 - 8 u
= 17 u - 70
= 17 x 28 - 70
= 476 - 70
= $406

Answer(s): $406