Xuan, Penelope and Xylia had a sum of money. The amount of money Xuan had was ³₄ of the amount of money Penelope had. The ratio of the amount of money Penelope had to the total amount of money Xylia and Penelope had was 2: 5. After Xylia gave $71 to Penelope, she had as much money as Penelope. How much more money did Xylia have than Xuan in the end?

Xuan	Penelope	Xylia
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Xuan	Penelope	Xylia
Before	3 u	4 u	6 u
Change	No change	+ 71	- 71
After	3 u	4 u + 71	6 u - 71

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

6 u - 71 = 4 u + 71
6 u - 4 u = 71 + 71 
2 u = 142

1 u = 142 ÷ 2 = 71

Amount that Xylia had more than Xuan in the end
= 6 u - 71 - 3 u
= 3 u - 71
= 3 x 71 - 71
= 213 - 71
= $142

Answer(s): $142