Pamela, Shiyun and Mary had a sum of money. The amount of money Pamela had was ²₃ of the amount of money Shiyun had. The ratio of the amount of money Shiyun had to the total amount of money Mary and Shiyun had was 2: 5. After Mary gave $69 to Shiyun, she had as much money as Shiyun. How much more money did Mary have than Pamela in the end?

Pamela	Shiyun	Mary
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	3x3 = 9 u
4 u	6 u	9 u

The amount that Shiyun had is the repeated identity. Make the amount that Shiyun had the same.  LCM of 3 and 2 is 6.

	Pamela	Shiyun	Mary
Before	4 u	6 u	9 u
Change	No change	+ 69	- 69
After	4 u	6 u + 69	9 u - 69

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

9 u - 69 = 6 u + 69
9 u - 6 u = 69 + 69 
3 u = 138

1 u = 138 ÷ 3 = 46

Amount that Mary had more than Pamela in the end
= 9 u - 69 - 4 u
= 5 u - 69
= 5 x 46 - 69
= 230 - 69
= $161

Answer(s): $161