Jade, Anna and Shiyun had a sum of money. The amount of money Jade had was ²₅ of the amount of money Anna had. The ratio of the amount of money Anna had to the total amount of money Shiyun and Anna had was 2: 7. After Shiyun gave $45 to Anna, she had as much money as Anna. How much more money did Shiyun have than Jade in the end?

Jade	Anna	Shiyun
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	5x5 = 25 u
4 u	10 u	25 u

The amount that Anna had is the repeated identity. Make the amount that Anna had the same.  LCM of 5 and 2 is 10.

	Jade	Anna	Shiyun
Before	4 u	10 u	25 u
Change	No change	+ 45	- 45
After	4 u	10 u + 45	25 u - 45

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

25 u - 45 = 10 u + 45
25 u - 10 u = 45 + 45 
15 u = 90

1 u = 90 ÷ 15 = 6

Amount that Shiyun had more than Jade in the end
= 25 u - 45 - 4 u
= 21 u - 45
= 21 x 6 - 45
= 126 - 45
= $81

Answer(s): $81