Tammy, Gillian and Rachel had a sum of money. The amount of money Tammy had was ⁴₅ of the amount of money Gillian had. The ratio of the amount of money Gillian had to the total amount of money Rachel and Gillian had was 2: 5. After Rachel gave $50 to Gillian, she had as much money as Gillian. How much more money did Rachel have than Tammy in the end?

Tammy	Gillian	Rachel
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
8 u	10 u	15 u

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

	Tammy	Gillian	Rachel
Before	8 u	10 u	15 u
Change	No change	+ 50	- 50
After	8 u	10 u + 50	15 u - 50

The amount that Rachel and Gillian had in the end is the same.

15 u - 50 = 10 u + 50
15 u - 10 u = 50 + 50 
5 u = 100

1 u = 100 ÷ 5 = 20

Amount that Rachel had more than Tammy in the end
= 15 u - 50 - 8 u
= 7 u - 50
= 7 x 20 - 50
= 140 - 50
= $90

Answer(s): $90