Min, Rachel and Irene had a sum of money. The amount of money Min had was ²₅ of the amount of money Rachel had. The ratio of the amount of money Rachel had to the total amount of money Irene and Rachel had was 3: 7. After Irene gave $85 to Rachel, she had as much money as Rachel. How much more money did Irene have than Min in the end?

Min	Rachel	Irene
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
6 u	15 u	20 u

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

	Min	Rachel	Irene
Before	6 u	15 u	20 u
Change	No change	+ 85	- 85
After	6 u	15 u + 85	20 u - 85

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

20 u - 85 = 15 u + 85
20 u - 15 u = 85 + 85 
5 u = 170

1 u = 170 ÷ 5 = 34

Amount that Irene had more than Min in the end
= 20 u - 85 - 6 u
= 14 u - 85
= 14 x 34 - 85
= 476 - 85
= $391

Answer(s): $391