Rachel, Lucy and Jane had a sum of money. The amount of money Rachel had was ³₄ of the amount of money Lucy had. The ratio of the amount of money Lucy had to the total amount of money Jane and Lucy had was 2: 9. After Jane gave $40 to Lucy, she had as much money as Lucy. How much more money did Jane have than Rachel in the end?

Rachel	Lucy	Jane
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	7x2 = 14 u
3 u	4 u	14 u

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

	Rachel	Lucy	Jane
Before	3 u	4 u	14 u
Change	No change	+ 40	- 40
After	3 u	4 u + 40	14 u - 40

The amount that Jane and Lucy had in the end is the same.

14 u - 40 = 4 u + 40
14 u - 4 u = 40 + 40 
10 u = 80

1 u = 80 ÷ 10 = 8

Amount that Jane had more than Rachel in the end
= 14 u - 40 - 3 u
= 11 u - 40
= 11 x 8 - 40
= 88 - 40
= $48

Answer(s): $48