Emily, Lucy and Victoria had a sum of money. The amount of money Emily had was ³₄ of the amount of money Lucy had. The ratio of the amount of money Lucy had to the total amount of money Victoria and Lucy had was 2: 5. After Victoria gave $58 to Lucy, she had as much money as Lucy. How much more money did Victoria have than Emily in the end?

Emily	Lucy	Victoria
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

The amount that Lucy had is the repeated identity. Make the amount that Lucy had the same.  LCM of 4 and 2 is 4.

	Emily	Lucy	Victoria
Before	3 u	4 u	6 u
Change	No change	+ 58	- 58
After	3 u	4 u + 58	6 u - 58

The amount that Victoria and Lucy had in the end is the same.

6 u - 58 = 4 u + 58
6 u - 4 u = 58 + 58 
2 u = 116

1 u = 116 ÷ 2 = 58

Amount that Victoria had more than Emily in the end
= 6 u - 58 - 3 u
= 3 u - 58
= 3 x 58 - 58
= 174 - 58
= $116

Answer(s): $116