Shannon, Lynn and Elyse had a sum of money. The amount of money Shannon had was ³₄ of the amount of money Lynn had. The ratio of the amount of money Lynn had to the total amount of money Elyse and Lynn had was 2: 5. After Elyse gave $23 to Lynn, she had as much money as Lynn. How much more money did Elyse have than Shannon in the end?

Shannon	Lynn	Elyse
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Shannon	Lynn	Elyse
Before	3 u	4 u	6 u
Change	No change	+ 23	- 23
After	3 u	4 u + 23	6 u - 23

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

6 u - 23 = 4 u + 23
6 u - 4 u = 23 + 23 
2 u = 46

1 u = 46 ÷ 2 = 23

Amount that Elyse had more than Shannon in the end
= 6 u - 23 - 3 u
= 3 u - 23
= 3 x 23 - 23
= 69 - 23
= $46

Answer(s): $46