Cindy, Gwen and Kimberly had a sum of money. The amount of money Cindy had was ²₃ of the amount of money Gwen had. The ratio of the amount of money Gwen had to the total amount of money Kimberly and Gwen had was 4: 9. After Kimberly gave $84 to Gwen, she had as much money as Gwen. How much more money did Kimberly have than Cindy in the end?

Cindy	Gwen	Kimberly
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

The amount that Gwen had is the repeated identity. Make the amount that Gwen had the same.  LCM of 3 and 4 is 12.

	Cindy	Gwen	Kimberly
Before	8 u	12 u	15 u
Change	No change	+ 84	- 84
After	8 u	12 u + 84	15 u - 84

The amount that Kimberly and Gwen had in the end is the same.

15 u - 84 = 12 u + 84
15 u - 12 u = 84 + 84 
3 u = 168

1 u = 168 ÷ 3 = 56

Amount that Kimberly had more than Cindy in the end
= 15 u - 84 - 8 u
= 7 u - 84
= 7 x 56 - 84
= 392 - 84
= $308

Answer(s): $308