Raeann, Olivia and Rachel had a sum of money. The amount of money Raeann had was ³₄ of the amount of money Olivia had. The ratio of the amount of money Olivia had to the total amount of money Rachel and Olivia had was 3: 7. After Rachel gave $42 to Olivia, she had as much money as Olivia. How much more money did Rachel have than Raeann in the end?

Raeann	Olivia	Rachel
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

The amount that Olivia had is the repeated identity. Make the amount that Olivia had the same.  LCM of 4 and 3 is 12.

	Raeann	Olivia	Rachel
Before	9 u	12 u	16 u
Change	No change	+ 42	- 42
After	9 u	12 u + 42	16 u - 42

The amount that Rachel and Olivia had in the end is the same.

16 u - 42 = 12 u + 42
16 u - 12 u = 42 + 42 
4 u = 84

1 u = 84 ÷ 4 = 21

Amount that Rachel had more than Raeann in the end
= 16 u - 42 - 9 u
= 7 u - 42
= 7 x 21 - 42
= 147 - 42
= $105

Answer(s): $105