Xuan, Opal and Shiyun had a sum of money. The amount of money Xuan had was ³₄ of the amount of money Opal had. The ratio of the amount of money Opal had to the total amount of money Shiyun and Opal had was 2: 5. After Shiyun gave $97 to Opal, she had as much money as Opal. How much more money did Shiyun have than Xuan in the end?

Xuan	Opal	Shiyun
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Xuan	Opal	Shiyun
Before	3 u	4 u	6 u
Change	No change	+ 97	- 97
After	3 u	4 u + 97	6 u - 97

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

6 u - 97 = 4 u + 97
6 u - 4 u = 97 + 97 
2 u = 194

1 u = 194 ÷ 2 = 97

Amount that Shiyun had more than Xuan in the end
= 6 u - 97 - 3 u
= 3 u - 97
= 3 x 97 - 97
= 291 - 97
= $194

Answer(s): $194