Jane, Fanny and Olivia had a sum of money. The amount of money Jane had was ³₅ of the amount of money Fanny had. The ratio of the amount of money Fanny had to the total amount of money Olivia and Fanny had was 3: 7. After Olivia gave $5 to Fanny, she had as much money as Fanny. How much more money did Olivia have than Jane in the end?

Jane	Fanny	Olivia
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
9 u	15 u	20 u

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

	Jane	Fanny	Olivia
Before	9 u	15 u	20 u
Change	No change	+ 5	- 5
After	9 u	15 u + 5	20 u - 5

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

20 u - 5 = 15 u + 5
20 u - 15 u = 5 + 5 
5 u = 10

1 u = 10 ÷ 5 = 2

Amount that Olivia had more than Jane in the end
= 20 u - 5 - 9 u
= 11 u - 5
= 11 x 2 - 5
= 22 - 5
= $17

Answer(s): $17