Linda, Vanessa and Lynn had a sum of money. The amount of money Linda had was ³₄ of the amount of money Vanessa had. The ratio of the amount of money Vanessa had to the total amount of money Lynn and Vanessa had was 2: 7. After Lynn gave $39 to Vanessa, she had as much money as Vanessa. How much more money did Lynn have than Linda in the end?

Linda	Vanessa	Lynn
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	5x2 = 10 u
3 u	4 u	10 u

The amount that Vanessa had is the repeated identity. Make the amount that Vanessa had the same.  LCM of 4 and 2 is 4.

	Linda	Vanessa	Lynn
Before	3 u	4 u	10 u
Change	No change	+ 39	- 39
After	3 u	4 u + 39	10 u - 39

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

10 u - 39 = 4 u + 39
10 u - 4 u = 39 + 39 
6 u = 78

1 u = 78 ÷ 6 = 13

Amount that Lynn had more than Linda in the end
= 10 u - 39 - 3 u
= 7 u - 39
= 7 x 13 - 39
= 91 - 39
= $52

Answer(s): $52