Tammy, Erika and Yoko had a sum of money. The amount of money Tammy had was ⁴₅ of the amount of money Erika had. The ratio of the amount of money Erika had to the total amount of money Yoko and Erika had was 2: 9. After Yoko gave $50 to Erika, she had as much money as Erika. How much more money did Yoko have than Tammy in the end?

Tammy	Erika	Yoko
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	7x5 = 35 u
8 u	10 u	35 u

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

	Tammy	Erika	Yoko
Before	8 u	10 u	35 u
Change	No change	+ 50	- 50
After	8 u	10 u + 50	35 u - 50

The amount that Yoko and Erika had in the end is the same.

35 u - 50 = 10 u + 50
35 u - 10 u = 50 + 50 
25 u = 100

1 u = 100 ÷ 25 = 4

Amount that Yoko had more than Tammy in the end
= 35 u - 50 - 8 u
= 27 u - 50
= 27 x 4 - 50
= 108 - 50
= $58

Answer(s): $58