Nicole, Usha and Cathy had a sum of money. The amount of money Nicole had was ³₅ of the amount of money Usha had. The ratio of the amount of money Usha had to the total amount of money Cathy and Usha had was 3: 8. After Cathy gave $20 to Usha, she had as much money as Usha. How much more money did Cathy have than Nicole in the end?

Nicole	Usha	Cathy
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
9 u	15 u	25 u

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

	Nicole	Usha	Cathy
Before	9 u	15 u	25 u
Change	No change	+ 20	- 20
After	9 u	15 u + 20	25 u - 20

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

25 u - 20 = 15 u + 20
25 u - 15 u = 20 + 20 
10 u = 40

1 u = 40 ÷ 10 = 4

Amount that Cathy had more than Nicole in the end
= 25 u - 20 - 9 u
= 16 u - 20
= 16 x 4 - 20
= 64 - 20
= $44

Answer(s): $44