Diana, Zoe and Tina had a sum of money. The amount of money Diana had was ³₄ of the amount of money Zoe had. The ratio of the amount of money Zoe had to the total amount of money Tina and Zoe had was 2: 7. After Tina gave $96 to Zoe, she had as much money as Zoe. How much more money did Tina have than Diana in the end?

Diana	Zoe	Tina
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	5x2 = 10 u
3 u	4 u	10 u

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

	Diana	Zoe	Tina
Before	3 u	4 u	10 u
Change	No change	+ 96	- 96
After	3 u	4 u + 96	10 u - 96

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

10 u - 96 = 4 u + 96
10 u - 4 u = 96 + 96 
6 u = 192

1 u = 192 ÷ 6 = 32

Amount that Tina had more than Diana in the end
= 10 u - 96 - 3 u
= 7 u - 96
= 7 x 32 - 96
= 224 - 96
= $128

Answer(s): $128