Tammy, Gwen and Zoe had a sum of money. The amount of money Tammy had was ²₃ of the amount of money Gwen had. The ratio of the amount of money Gwen had to the total amount of money Zoe and Gwen had was 2: 7. After Zoe gave $81 to Gwen, she had as much money as Gwen. How much more money did Zoe have than Tammy in the end?

Tammy	Gwen	Zoe
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	5x3 = 15 u
4 u	6 u	15 u

The amount that Gwen had is the repeated identity. Make the amount that Gwen had the same.  LCM of 3 and 2 is 6.

	Tammy	Gwen	Zoe
Before	4 u	6 u	15 u
Change	No change	+ 81	- 81
After	4 u	6 u + 81	15 u - 81

The amount that Zoe and Gwen had in the end is the same.

15 u - 81 = 6 u + 81
15 u - 6 u = 81 + 81 
9 u = 162

1 u = 162 ÷ 9 = 18

Amount that Zoe had more than Tammy in the end
= 15 u - 81 - 4 u
= 11 u - 81
= 11 x 18 - 81
= 198 - 81
= $117

Answer(s): $117