Gem, Tammy and Natalie had a sum of money. The amount of money Gem had was ³₄ of the amount of money Tammy had. The ratio of the amount of money Tammy had to the total amount of money Natalie and Tammy had was 3: 7. After Natalie gave $18 to Tammy, she had as much money as Tammy. How much more money did Natalie have than Gem in the end?

Gem	Tammy	Natalie
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

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

	Gem	Tammy	Natalie
Before	9 u	12 u	16 u
Change	No change	+ 18	- 18
After	9 u	12 u + 18	16 u - 18

The amount that Natalie and Tammy had in the end is the same.

16 u - 18 = 12 u + 18
16 u - 12 u = 18 + 18 
4 u = 36

1 u = 36 ÷ 4 = 9

Amount that Natalie had more than Gem in the end
= 16 u - 18 - 9 u
= 7 u - 18
= 7 x 9 - 18
= 63 - 18
= $45

Answer(s): $45