Gwen, Vanessa and Xylia had a sum of money. The amount of money Gwen had was ³₄ of the amount of money Vanessa had. The ratio of the amount of money Vanessa had to the total amount of money Xylia and Vanessa had was 2: 5. After Xylia gave $43 to Vanessa, she had as much money as Vanessa. How much more money did Xylia have than Gwen in the end?

Gwen	Vanessa	Xylia
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Gwen	Vanessa	Xylia
Before	3 u	4 u	6 u
Change	No change	+ 43	- 43
After	3 u	4 u + 43	6 u - 43

The amount that Xylia and Vanessa had in the end is the same.

6 u - 43 = 4 u + 43
6 u - 4 u = 43 + 43 
2 u = 86

1 u = 86 ÷ 2 = 43

Amount that Xylia had more than Gwen in the end
= 6 u - 43 - 3 u
= 3 u - 43
= 3 x 43 - 43
= 129 - 43
= $86

Answer(s): $86