Jean, Natalie and Roshel had a sum of money. The amount of money Jean had was ²₅ of the amount of money Natalie had. The ratio of the amount of money Natalie had to the total amount of money Roshel and Natalie had was 2: 9. After Roshel gave $75 to Natalie, she had as much money as Natalie. How much more money did Roshel have than Jean in the end?

Jean	Natalie	Roshel
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	7x5 = 35 u
4 u	10 u	35 u

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

	Jean	Natalie	Roshel
Before	4 u	10 u	35 u
Change	No change	+ 75	- 75
After	4 u	10 u + 75	35 u - 75

The amount that Roshel and Natalie had in the end is the same.

35 u - 75 = 10 u + 75
35 u - 10 u = 75 + 75 
25 u = 150

1 u = 150 ÷ 25 = 6

Amount that Roshel had more than Jean in the end
= 35 u - 75 - 4 u
= 31 u - 75
= 31 x 6 - 75
= 186 - 75
= $111

Answer(s): $111