Gem, Shannon and Min had a sum of money. The amount of money Gem had was ⁴₅ of the amount of money Shannon had. The ratio of the amount of money Shannon had to the total amount of money Min and Shannon had was 2: 5. After Min gave $90 to Shannon, she had as much money as Shannon. How much more money did Min have than Gem in the end?

Gem	Shannon	Min
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Gem	Shannon	Min
Before	8 u	10 u	15 u
Change	No change	+ 90	- 90
After	8 u	10 u + 90	15 u - 90

The amount that Min and Shannon had in the end is the same.

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

1 u = 180 ÷ 5 = 36

Amount that Min had more than Gem in the end
= 15 u - 90 - 8 u
= 7 u - 90
= 7 x 36 - 90
= 252 - 90
= $162

Answer(s): $162