Fanny, Raeann and Opal had a sum of money. The amount of money Fanny had was ⁴₅ of the amount of money Raeann had. The ratio of the amount of money Raeann had to the total amount of money Opal and Raeann had was 3: 7. After Opal gave $100 to Raeann, she had as much money as Raeann. How much more money did Opal have than Fanny in the end?

Fanny	Raeann	Opal
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Fanny	Raeann	Opal
Before	12 u	15 u	20 u
Change	No change	+ 100	- 100
After	12 u	15 u + 100	20 u - 100

The amount that Opal and Raeann had in the end is the same.

20 u - 100 = 15 u + 100
20 u - 15 u = 100 + 100 
5 u = 200

1 u = 200 ÷ 5 = 40

Amount that Opal had more than Fanny in the end
= 20 u - 100 - 12 u
= 8 u - 100
= 8 x 40 - 100
= 320 - 100
= $220

Answer(s): $220