Winnie, Marion and Julie had a sum of money. The amount of money Winnie had was ⁴₅ of the amount of money Marion had. The ratio of the amount of money Marion had to the total amount of money Julie and Marion had was 3: 8. After Julie gave $100 to Marion, she had as much money as Marion. How much more money did Julie have than Winnie in the end?

Winnie	Marion	Julie
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
12 u	15 u	25 u

The amount that Marion had is the repeated identity. Make the amount that Marion had the same.  LCM of 5 and 3 is 15.

	Winnie	Marion	Julie
Before	12 u	15 u	25 u
Change	No change	+ 100	- 100
After	12 u	15 u + 100	25 u - 100

The amount that Julie and Marion had in the end is the same.

25 u - 100 = 15 u + 100
25 u - 15 u = 100 + 100 
10 u = 200

1 u = 200 ÷ 10 = 20

Amount that Julie had more than Winnie in the end
= 25 u - 100 - 12 u
= 13 u - 100
= 13 x 20 - 100
= 260 - 100
= $160

Answer(s): $160