Irene, Sarah and Winnie had a sum of money. The amount of money Irene had was ³₄ of the amount of money Sarah had. The ratio of the amount of money Sarah had to the total amount of money Winnie and Sarah had was 2: 7. After Winnie gave $15 to Sarah, she had as much money as Sarah. How much more money did Winnie have than Irene in the end?

Irene	Sarah	Winnie
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	5x2 = 10 u
3 u	4 u	10 u

The amount that Sarah had is the repeated identity. Make the amount that Sarah had the same.  LCM of 4 and 2 is 4.

	Irene	Sarah	Winnie
Before	3 u	4 u	10 u
Change	No change	+ 15	- 15
After	3 u	4 u + 15	10 u - 15

The amount that Winnie and Sarah had in the end is the same.

10 u - 15 = 4 u + 15
10 u - 4 u = 15 + 15 
6 u = 30

1 u = 30 ÷ 6 = 5

Amount that Winnie had more than Irene in the end
= 10 u - 15 - 3 u
= 7 u - 15
= 7 x 5 - 15
= 35 - 15
= $20

Answer(s): $20