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

Tina	Cathy	Olivia
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Tina	Cathy	Olivia
Before	8 u	10 u	15 u
Change	No change	+ 5	- 5
After	8 u	10 u + 5	15 u - 5

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

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

1 u = 10 ÷ 5 = 2

Amount that Olivia had more than Tina in the end
= 15 u - 5 - 8 u
= 7 u - 5
= 7 x 2 - 5
= 14 - 5
= $9

Answer(s): $9