Julie, Rachel and Sabrina had a sum of money. The amount of money Julie had was ³₄ of the amount of money Rachel had. The ratio of the amount of money Rachel had to the total amount of money Sabrina and Rachel had was 2: 9. After Sabrina gave $85 to Rachel, she had as much money as Rachel. How much more money did Sabrina have than Julie in the end?

Julie	Rachel	Sabrina
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	7x2 = 14 u
3 u	4 u	14 u

The amount that Rachel had is the repeated identity. Make the amount that Rachel had the same.  LCM of 4 and 2 is 4.

	Julie	Rachel	Sabrina
Before	3 u	4 u	14 u
Change	No change	+ 85	- 85
After	3 u	4 u + 85	14 u - 85

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

14 u - 85 = 4 u + 85
14 u - 4 u = 85 + 85 
10 u = 170

1 u = 170 ÷ 10 = 17

Amount that Sabrina had more than Julie in the end
= 14 u - 85 - 3 u
= 11 u - 85
= 11 x 17 - 85
= 187 - 85
= $102

Answer(s): $102