Ivory, Opal and Yen had a sum of money. The amount of money Ivory had was ³₄ of the amount of money Opal had. The ratio of the amount of money Opal had to the total amount of money Yen and Opal had was 3: 8. After Yen gave $20 to Opal, she had as much money as Opal. How much more money did Yen have than Ivory in the end?

Ivory	Opal	Yen
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	5x4 = 20 u
9 u	12 u	20 u

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

	Ivory	Opal	Yen
Before	9 u	12 u	20 u
Change	No change	+ 20	- 20
After	9 u	12 u + 20	20 u - 20

The amount that Yen and Opal had in the end is the same.

20 u - 20 = 12 u + 20
20 u - 12 u = 20 + 20 
8 u = 40

1 u = 40 ÷ 8 = 5

Amount that Yen had more than Ivory in the end
= 20 u - 20 - 9 u
= 11 u - 20
= 11 x 5 - 20
= 55 - 20
= $35

Answer(s): $35