Marion, Pamela and Gem had a sum of money. The amount of money Marion had was ⁴₅ of the amount of money Pamela had. The ratio of the amount of money Pamela had to the total amount of money Gem and Pamela had was 3: 8. After Gem gave $80 to Pamela, she had as much money as Pamela. How much more money did Gem have than Marion in the end?

Marion	Pamela	Gem
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
12 u	15 u	25 u

The amount that Pamela had is the repeated identity. Make the amount that Pamela had the same.  LCM of 5 and 3 is 15.

	Marion	Pamela	Gem
Before	12 u	15 u	25 u
Change	No change	+ 80	- 80
After	12 u	15 u + 80	25 u - 80

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

25 u - 80 = 15 u + 80
25 u - 15 u = 80 + 80 
10 u = 160

1 u = 160 ÷ 10 = 16

Amount that Gem had more than Marion in the end
= 25 u - 80 - 12 u
= 13 u - 80
= 13 x 16 - 80
= 208 - 80
= $128

Answer(s): $128