Nicole, Julie and Usha had a sum of money. The amount of money Nicole had was ⁴₅ of the amount of money Julie had. The ratio of the amount of money Julie had to the total amount of money Usha and Julie had was 3: 8. After Usha gave $15 to Julie, she had as much money as Julie. How much more money did Usha have than Nicole in the end?

Nicole	Julie	Usha
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
12 u	15 u	25 u

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

	Nicole	Julie	Usha
Before	12 u	15 u	25 u
Change	No change	+ 15	- 15
After	12 u	15 u + 15	25 u - 15

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

25 u - 15 = 15 u + 15
25 u - 15 u = 15 + 15 
10 u = 30

1 u = 30 ÷ 10 = 3

Amount that Usha had more than Nicole in the end
= 25 u - 15 - 12 u
= 13 u - 15
= 13 x 3 - 15
= 39 - 15
= $24

Answer(s): $24