Joelle, Natalie and Anna had a sum of money. The amount of money Joelle had was ⁴₅ of the amount of money Natalie had. The ratio of the amount of money Natalie had to the total amount of money Anna and Natalie had was 3: 7. After Anna gave $45 to Natalie, she had as much money as Natalie. How much more money did Anna have than Joelle in the end?

Joelle	Natalie	Anna
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Joelle	Natalie	Anna
Before	12 u	15 u	20 u
Change	No change	+ 45	- 45
After	12 u	15 u + 45	20 u - 45

The amount that Anna and Natalie had in the end is the same.

20 u - 45 = 15 u + 45
20 u - 15 u = 45 + 45 
5 u = 90

1 u = 90 ÷ 5 = 18

Amount that Anna had more than Joelle in the end
= 20 u - 45 - 12 u
= 8 u - 45
= 8 x 18 - 45
= 144 - 45
= $99

Answer(s): $99