Opal, Risa and Diana had a sum of money. The amount of money Opal had was ²₃ of the amount of money Risa had. The ratio of the amount of money Risa had to the total amount of money Diana and Risa had was 4: 9. After Diana gave $33 to Risa, she had as much money as Risa. How much more money did Diana have than Opal in the end?

Opal	Risa	Diana
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

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

	Opal	Risa	Diana
Before	8 u	12 u	15 u
Change	No change	+ 33	- 33
After	8 u	12 u + 33	15 u - 33

The amount that Diana and Risa had in the end is the same.

15 u - 33 = 12 u + 33
15 u - 12 u = 33 + 33 
3 u = 66

1 u = 66 ÷ 3 = 22

Amount that Diana had more than Opal in the end
= 15 u - 33 - 8 u
= 7 u - 33
= 7 x 22 - 33
= 154 - 33
= $121

Answer(s): $121