Wendy, Kathy and Kylie had a sum of money. The amount of money Wendy had was ³₄ of the amount of money Kathy had. The ratio of the amount of money Kathy had to the total amount of money Kylie and Kathy had was 3: 8. After Kylie gave $64 to Kathy, she had as much money as Kathy. How much more money did Kylie have than Wendy in the end?

Wendy	Kathy	Kylie
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	5x4 = 20 u
9 u	12 u	20 u

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

	Wendy	Kathy	Kylie
Before	9 u	12 u	20 u
Change	No change	+ 64	- 64
After	9 u	12 u + 64	20 u - 64

The amount that Kylie and Kathy had in the end is the same.

20 u - 64 = 12 u + 64
20 u - 12 u = 64 + 64 
8 u = 128

1 u = 128 ÷ 8 = 16

Amount that Kylie had more than Wendy in the end
= 20 u - 64 - 9 u
= 11 u - 64
= 11 x 16 - 64
= 176 - 64
= $112

Answer(s): $112