Min, Lucy and Mary had a sum of money. The amount of money Min had was ³₅ of the amount of money Lucy had. The ratio of the amount of money Lucy had to the total amount of money Mary and Lucy had was 4: 9. After Mary gave $95 to Lucy, she had as much money as Lucy. How much more money did Mary have than Min in the end?

Min	Lucy	Mary
3x4 = 12 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
12 u	20 u	25 u

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

	Min	Lucy	Mary
Before	12 u	20 u	25 u
Change	No change	+ 95	- 95
After	12 u	20 u + 95	25 u - 95

The amount that Mary and Lucy had in the end is the same.

25 u - 95 = 20 u + 95
25 u - 20 u = 95 + 95 
5 u = 190

1 u = 190 ÷ 5 = 38

Amount that Mary had more than Min in the end
= 25 u - 95 - 12 u
= 13 u - 95
= 13 x 38 - 95
= 494 - 95
= $399

Answer(s): $399