Penelope, Barbara and Eva had a sum of money. The amount of money Penelope had was ⁴₅ of the amount of money Barbara had. The ratio of the amount of money Barbara had to the total amount of money Eva and Barbara had was 2: 9. After Eva gave $25 to Barbara, she had as much money as Barbara. How much more money did Eva have than Penelope in the end?

Penelope	Barbara	Eva
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	7x5 = 35 u
8 u	10 u	35 u

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

	Penelope	Barbara	Eva
Before	8 u	10 u	35 u
Change	No change	+ 25	- 25
After	8 u	10 u + 25	35 u - 25

The amount that Eva and Barbara had in the end is the same.

35 u - 25 = 10 u + 25
35 u - 10 u = 25 + 25 
25 u = 50

1 u = 50 ÷ 25 = 2

Amount that Eva had more than Penelope in the end
= 35 u - 25 - 8 u
= 27 u - 25
= 27 x 2 - 25
= 54 - 25
= $29

Answer(s): $29