Dana, Marion and Lynn had a sum of money. The amount of money Dana had was ⁴₅ of the amount of money Marion had. The ratio of the amount of money Marion had to the total amount of money Lynn and Marion had was 3: 7. After Lynn gave $20 to Marion, she had as much money as Marion. How much more money did Lynn have than Dana in the end?

Dana	Marion	Lynn
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

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

	Dana	Marion	Lynn
Before	12 u	15 u	20 u
Change	No change	+ 20	- 20
After	12 u	15 u + 20	20 u - 20

The amount that Lynn and Marion had in the end is the same.

20 u - 20 = 15 u + 20
20 u - 15 u = 20 + 20 
5 u = 40

1 u = 40 ÷ 5 = 8

Amount that Lynn had more than Dana in the end
= 20 u - 20 - 12 u
= 8 u - 20
= 8 x 8 - 20
= 64 - 20
= $44

Answer(s): $44