Esther, Jen and Gem had a sum of money. The amount of money Esther had was ⁴₅ of the amount of money Jen had. The ratio of the amount of money Jen had to the total amount of money Gem and Jen had was 2: 7. After Gem gave $90 to Jen, she had as much money as Jen. How much more money did Gem have than Esther in the end?

Esther	Jen	Gem
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	5x5 = 25 u
8 u	10 u	25 u

The amount that Jen had is the repeated identity. Make the amount that Jen had the same.  LCM of 5 and 2 is 10.

	Esther	Jen	Gem
Before	8 u	10 u	25 u
Change	No change	+ 90	- 90
After	8 u	10 u + 90	25 u - 90

The amount that Gem and Jen had in the end is the same.

25 u - 90 = 10 u + 90
25 u - 10 u = 90 + 90 
15 u = 180

1 u = 180 ÷ 15 = 12

Amount that Gem had more than Esther in the end
= 25 u - 90 - 8 u
= 17 u - 90
= 17 x 12 - 90
= 204 - 90
= $114

Answer(s): $114