Emma, Xandra and Emily had a sum of money. The amount of money Emma had was ³₄ of the amount of money Xandra had. The ratio of the amount of money Xandra had to the total amount of money Emily and Xandra had was 3: 8. After Emily gave $12 to Xandra, she had as much money as Xandra. How much more money did Emily have than Emma in the end?

Emma	Xandra	Emily
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	5x4 = 20 u
9 u	12 u	20 u

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

	Emma	Xandra	Emily
Before	9 u	12 u	20 u
Change	No change	+ 12	- 12
After	9 u	12 u + 12	20 u - 12

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

20 u - 12 = 12 u + 12
20 u - 12 u = 12 + 12 
8 u = 24

1 u = 24 ÷ 8 = 3

Amount that Emily had more than Emma in the end
= 20 u - 12 - 9 u
= 11 u - 12
= 11 x 3 - 12
= 33 - 12
= $21

Answer(s): $21