Kathy, Penelope and Opal had a sum of money. The amount of money Kathy had was ²₃ of the amount of money Penelope had. The ratio of the amount of money Penelope had to the total amount of money Opal and Penelope had was 2: 7. After Opal gave $18 to Penelope, she had as much money as Penelope. How much more money did Opal have than Kathy in the end?

Kathy	Penelope	Opal
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	5x3 = 15 u
4 u	6 u	15 u

The amount that Penelope had is the repeated identity. Make the amount that Penelope had the same.  LCM of 3 and 2 is 6.

	Kathy	Penelope	Opal
Before	4 u	6 u	15 u
Change	No change	+ 18	- 18
After	4 u	6 u + 18	15 u - 18

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

15 u - 18 = 6 u + 18
15 u - 6 u = 18 + 18 
9 u = 36

1 u = 36 ÷ 9 = 4

Amount that Opal had more than Kathy in the end
= 15 u - 18 - 4 u
= 11 u - 18
= 11 x 4 - 18
= 44 - 18
= $26

Answer(s): $26