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

Gem	Lucy	Eva
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Gem	Lucy	Eva
Before	8 u	10 u	15 u
Change	No change	+ 45	- 45
After	8 u	10 u + 45	15 u - 45

The amount that Eva and Lucy had in the end is the same.

15 u - 45 = 10 u + 45
15 u - 10 u = 45 + 45 
5 u = 90

1 u = 90 ÷ 5 = 18

Amount that Eva had more than Gem in the end
= 15 u - 45 - 8 u
= 7 u - 45
= 7 x 18 - 45
= 126 - 45
= $81

Answer(s): $81