Xylia, Olivia and Hilda had a sum of money. The amount of money Xylia had was ⁴₅ of the amount of money Olivia had. The ratio of the amount of money Olivia had to the total amount of money Hilda and Olivia had was 2: 5. After Hilda gave $25 to Olivia, she had as much money as Olivia. How much more money did Hilda have than Xylia in the end?

Xylia	Olivia	Hilda
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Xylia	Olivia	Hilda
Before	8 u	10 u	15 u
Change	No change	+ 25	- 25
After	8 u	10 u + 25	15 u - 25

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

15 u - 25 = 10 u + 25
15 u - 10 u = 25 + 25 
5 u = 50

1 u = 50 ÷ 5 = 10

Amount that Hilda had more than Xylia in the end
= 15 u - 25 - 8 u
= 7 u - 25
= 7 x 10 - 25
= 70 - 25
= $45

Answer(s): $45