Betty, Cathy and Barbara had a sum of money. The amount of money Betty had was ³₅ of the amount of money Cathy had. The ratio of the amount of money Cathy had to the total amount of money Barbara and Cathy had was 3: 8. After Barbara gave $65 to Cathy, she had as much money as Cathy. How much more money did Barbara have than Betty in the end?

Betty	Cathy	Barbara
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
9 u	15 u	25 u

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

	Betty	Cathy	Barbara
Before	9 u	15 u	25 u
Change	No change	+ 65	- 65
After	9 u	15 u + 65	25 u - 65

The amount that Barbara and Cathy had in the end is the same.

25 u - 65 = 15 u + 65
25 u - 15 u = 65 + 65 
10 u = 130

1 u = 130 ÷ 10 = 13

Amount that Barbara had more than Betty in the end
= 25 u - 65 - 9 u
= 16 u - 65
= 16 x 13 - 65
= 208 - 65
= $143

Answer(s): $143