Shiyun, Winnie and Diana had a sum of money. The amount of money Shiyun had was ³₄ of the amount of money Winnie had. The ratio of the amount of money Winnie had to the total amount of money Diana and Winnie had was 3: 7. After Diana gave $80 to Winnie, she had as much money as Winnie. How much more money did Diana have than Shiyun in the end?

Shiyun	Winnie	Diana
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

The amount that Winnie had is the repeated identity. Make the amount that Winnie had the same.  LCM of 4 and 3 is 12.

	Shiyun	Winnie	Diana
Before	9 u	12 u	16 u
Change	No change	+ 80	- 80
After	9 u	12 u + 80	16 u - 80

The amount that Diana and Winnie had in the end is the same.

16 u - 80 = 12 u + 80
16 u - 12 u = 80 + 80 
4 u = 160

1 u = 160 ÷ 4 = 40

Amount that Diana had more than Shiyun in the end
= 16 u - 80 - 9 u
= 7 u - 80
= 7 x 40 - 80
= 280 - 80
= $200

Answer(s): $200