Cathy, Emily and Tammy had a sum of money. The amount of money Cathy had was ³₄ of the amount of money Emily had. The ratio of the amount of money Emily had to the total amount of money Tammy and Emily had was 2: 5. After Tammy gave $41 to Emily, she had as much money as Emily. How much more money did Tammy have than Cathy in the end?

Cathy	Emily	Tammy
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

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

	Cathy	Emily	Tammy
Before	3 u	4 u	6 u
Change	No change	+ 41	- 41
After	3 u	4 u + 41	6 u - 41

The amount that Tammy and Emily had in the end is the same.

6 u - 41 = 4 u + 41
6 u - 4 u = 41 + 41 
2 u = 82

1 u = 82 ÷ 2 = 41

Amount that Tammy had more than Cathy in the end
= 6 u - 41 - 3 u
= 3 u - 41
= 3 x 41 - 41
= 123 - 41
= $82

Answer(s): $82