Shiyun, Kathy and Jane had a sum of money. The amount of money Shiyun had was ³₅ of the amount of money Kathy had. The ratio of the amount of money Kathy had to the total amount of money Jane and Kathy had was 4: 9. After Jane gave $35 to Kathy, she had as much money as Kathy. How much more money did Jane have than Shiyun in the end?

Shiyun	Kathy	Jane
3x4 = 12 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
12 u	20 u	25 u

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

	Shiyun	Kathy	Jane
Before	12 u	20 u	25 u
Change	No change	+ 35	- 35
After	12 u	20 u + 35	25 u - 35

The amount that Jane and Kathy had in the end is the same.

25 u - 35 = 20 u + 35
25 u - 20 u = 35 + 35 
5 u = 70

1 u = 70 ÷ 5 = 14

Amount that Jane had more than Shiyun in the end
= 25 u - 35 - 12 u
= 13 u - 35
= 13 x 14 - 35
= 182 - 35
= $147

Answer(s): $147