Tiffany, Gem and Nicole had a sum of money. The amount of money Tiffany had was ³₅ of the amount of money Gem had. The ratio of the amount of money Gem had to the total amount of money Nicole and Gem had was 4: 9. After Nicole gave $65 to Gem, she had as much money as Gem. How much more money did Nicole have than Tiffany in the end?

Tiffany	Gem	Nicole
3x4 = 12 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
12 u	20 u	25 u

The amount that Gem had is the repeated identity. Make the amount that Gem had the same.  LCM of 5 and 4 is 20.

	Tiffany	Gem	Nicole
Before	12 u	20 u	25 u
Change	No change	+ 65	- 65
After	12 u	20 u + 65	25 u - 65

The amount that Nicole and Gem had in the end is the same.

25 u - 65 = 20 u + 65
25 u - 20 u = 65 + 65 
5 u = 130

1 u = 130 ÷ 5 = 26

Amount that Nicole had more than Tiffany in the end
= 25 u - 65 - 12 u
= 13 u - 65
= 13 x 26 - 65
= 338 - 65
= $273

Answer(s): $273