Lucy, Mary and Shiyun had a sum of money. The amount of money Lucy had was ³₄ of the amount of money Mary had. The ratio of the amount of money Mary had to the total amount of money Shiyun and Mary had was 2: 5. After Shiyun gave $45 to Mary, she had as much money as Mary. How much more money did Shiyun have than Lucy in the end?

Lucy	Mary	Shiyun
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Lucy	Mary	Shiyun
Before	3 u	4 u	6 u
Change	No change	+ 45	- 45
After	3 u	4 u + 45	6 u - 45

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

6 u - 45 = 4 u + 45
6 u - 4 u = 45 + 45 
2 u = 90

1 u = 90 ÷ 2 = 45

Amount that Shiyun had more than Lucy in the end
= 6 u - 45 - 3 u
= 3 u - 45
= 3 x 45 - 45
= 135 - 45
= $90

Answer(s): $90