Gillian, Erika and Barbara had a sum of money. The amount of money Gillian had was ³₅ of the amount of money Erika had. The ratio of the amount of money Erika had to the total amount of money Barbara and Erika had was 4: 9. After Barbara gave $80 to Erika, she had as much money as Erika. How much more money did Barbara have than Gillian in the end?

Gillian	Erika	Barbara
3x4 = 12 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
12 u	20 u	25 u

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

	Gillian	Erika	Barbara
Before	12 u	20 u	25 u
Change	No change	+ 80	- 80
After	12 u	20 u + 80	25 u - 80

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

25 u - 80 = 20 u + 80
25 u - 20 u = 80 + 80 
5 u = 160

1 u = 160 ÷ 5 = 32

Amount that Barbara had more than Gillian in the end
= 25 u - 80 - 12 u
= 13 u - 80
= 13 x 32 - 80
= 416 - 80
= $336

Answer(s): $336