Gem, Jane and Tiffany had a sum of money. The amount of money Gem had was ³₅ of the amount of money Jane had. The ratio of the amount of money Jane had to the total amount of money Tiffany and Jane had was 2: 5. After Tiffany gave $30 to Jane, she had as much money as Jane. How much more money did Tiffany have than Gem in the end?

Gem	Jane	Tiffany
3x2 = 6 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
6 u	10 u	15 u

The amount that Jane had is the repeated identity. Make the amount that Jane had the same.  LCM of 5 and 2 is 10.

	Gem	Jane	Tiffany
Before	6 u	10 u	15 u
Change	No change	+ 30	- 30
After	6 u	10 u + 30	15 u - 30

The amount that Tiffany and Jane had in the end is the same.

15 u - 30 = 10 u + 30
15 u - 10 u = 30 + 30 
5 u = 60

1 u = 60 ÷ 5 = 12

Amount that Tiffany had more than Gem in the end
= 15 u - 30 - 6 u
= 9 u - 30
= 9 x 12 - 30
= 108 - 30
= $78

Answer(s): $78