Xuan, Tammy and Elyse had a sum of money. The amount of money Xuan had was ²₅ of the amount of money Tammy had. The ratio of the amount of money Tammy had to the total amount of money Elyse and Tammy had was 3: 7. After Elyse gave $80 to Tammy, she had as much money as Tammy. How much more money did Elyse have than Xuan in the end?

Xuan	Tammy	Elyse
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
6 u	15 u	20 u

The amount that Tammy had is the repeated identity. Make the amount that Tammy had the same.  LCM of 5 and 3 is 15.

	Xuan	Tammy	Elyse
Before	6 u	15 u	20 u
Change	No change	+ 80	- 80
After	6 u	15 u + 80	20 u - 80

The amount that Elyse and Tammy had in the end is the same.

20 u - 80 = 15 u + 80
20 u - 15 u = 80 + 80 
5 u = 160

1 u = 160 ÷ 5 = 32

Amount that Elyse had more than Xuan in the end
= 20 u - 80 - 6 u
= 14 u - 80
= 14 x 32 - 80
= 448 - 80
= $368

Answer(s): $368