Anna, Penelope and Linda had a sum of money. The amount of money Anna 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 Linda and Penelope had was 2: 5. After Linda gave $90 to Penelope, she had as much money as Penelope. How much more money did Linda have than Anna in the end?

Anna	Penelope	Linda
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	3x3 = 9 u
4 u	6 u	9 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.

	Anna	Penelope	Linda
Before	4 u	6 u	9 u
Change	No change	+ 90	- 90
After	4 u	6 u + 90	9 u - 90

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

9 u - 90 = 6 u + 90
9 u - 6 u = 90 + 90 
3 u = 180

1 u = 180 ÷ 3 = 60

Amount that Linda had more than Anna in the end
= 9 u - 90 - 4 u
= 5 u - 90
= 5 x 60 - 90
= 300 - 90
= $210

Answer(s): $210