Jean, Sarah and Kylie had a sum of money. The amount of money Jean had was ²₅ of the amount of money Sarah had. The ratio of the amount of money Sarah had to the total amount of money Kylie and Sarah had was 4: 9. After Kylie gave $100 to Sarah, she had as much money as Sarah. How much more money did Kylie have than Jean in the end?

Jean	Sarah	Kylie
2x4 = 8 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
8 u	20 u	25 u

The amount that Sarah had is the repeated identity. Make the amount that Sarah had the same.  LCM of 5 and 4 is 20.

	Jean	Sarah	Kylie
Before	8 u	20 u	25 u
Change	No change	+ 100	- 100
After	8 u	20 u + 100	25 u - 100

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

25 u - 100 = 20 u + 100
25 u - 20 u = 100 + 100 
5 u = 200

1 u = 200 ÷ 5 = 40

Amount that Kylie had more than Jean in the end
= 25 u - 100 - 8 u
= 17 u - 100
= 17 x 40 - 100
= 680 - 100
= $580

Answer(s): $580