Rachel, Emma and Penelope had a sum of money. The amount of money Rachel had was ²₅ of the amount of money Emma had. The ratio of the amount of money Emma had to the total amount of money Penelope and Emma had was 3: 8. After Penelope gave $100 to Emma, she had as much money as Emma. How much more money did Penelope have than Rachel in the end?

Rachel	Emma	Penelope
2x3 = 6 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
6 u	15 u	25 u

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

	Rachel	Emma	Penelope
Before	6 u	15 u	25 u
Change	No change	+ 100	- 100
After	6 u	15 u + 100	25 u - 100

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

25 u - 100 = 15 u + 100
25 u - 15 u = 100 + 100 
10 u = 200

1 u = 200 ÷ 10 = 20

Amount that Penelope had more than Rachel in the end
= 25 u - 100 - 6 u
= 19 u - 100
= 19 x 20 - 100
= 380 - 100
= $280

Answer(s): $280