Kathy, Olivia and Emma had a sum of money. The amount of money Kathy had was ²₅ of the amount of money Olivia had. The ratio of the amount of money Olivia had to the total amount of money Emma and Olivia had was 3: 8. After Emma gave $70 to Olivia, she had as much money as Olivia. How much more money did Emma have than Kathy in the end?

Kathy	Olivia	Emma
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
6 u	15 u	25 u

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

	Kathy	Olivia	Emma
Before	6 u	15 u	25 u
Change	No change	+ 70	- 70
After	6 u	15 u + 70	25 u - 70

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

25 u - 70 = 15 u + 70
25 u - 15 u = 70 + 70 
10 u = 140

1 u = 140 ÷ 10 = 14

Amount that Emma had more than Kathy in the end
= 25 u - 70 - 6 u
= 19 u - 70
= 19 x 14 - 70
= 266 - 70
= $196

Answer(s): $196