Linda, Winnie and Olivia had a sum of money. The amount of money Linda had was ³₄ of the amount of money Winnie had. The ratio of the amount of money Winnie had to the total amount of money Olivia and Winnie had was 3: 7. After Olivia gave $48 to Winnie, she had as much money as Winnie. How much more money did Olivia have than Linda in the end?

Linda	Winnie	Olivia
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

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

	Linda	Winnie	Olivia
Before	9 u	12 u	16 u
Change	No change	+ 48	- 48
After	9 u	12 u + 48	16 u - 48

The amount that Olivia and Winnie had in the end is the same.

16 u - 48 = 12 u + 48
16 u - 12 u = 48 + 48 
4 u = 96

1 u = 96 ÷ 4 = 24

Amount that Olivia had more than Linda in the end
= 16 u - 48 - 9 u
= 7 u - 48
= 7 x 24 - 48
= 168 - 48
= $120

Answer(s): $120