Esther, Wendy and Tina had a sum of money. The amount of money Esther had was ⁴₅ of the amount of money Wendy had. The ratio of the amount of money Wendy had to the total amount of money Tina and Wendy had was 4: 9. After Tina gave $55 to Wendy, she had as much money as Wendy. How much more money did Tina have than Esther in the end?

Esther	Wendy	Tina
4x4 = 16 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
16 u	20 u	25 u

The amount that Wendy had is the repeated identity. Make the amount that Wendy had the same.  LCM of 5 and 4 is 20.

	Esther	Wendy	Tina
Before	16 u	20 u	25 u
Change	No change	+ 55	- 55
After	16 u	20 u + 55	25 u - 55

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

25 u - 55 = 20 u + 55
25 u - 20 u = 55 + 55 
5 u = 110

1 u = 110 ÷ 5 = 22

Amount that Tina had more than Esther in the end
= 25 u - 55 - 16 u
= 9 u - 55
= 9 x 22 - 55
= 198 - 55
= $143

Answer(s): $143