Vanessa had $325 less than Carl. Vanessa spent ¹₃ of her money and Carl spent ⁴₇ of his money. In the end, Carl and Vanessa had the same amount of money left. Find the amount of money Carl had at first.

	Vanessa	Carl	Difference
Before	3x3 = 9 u	7x2 = 14 u	5 u
Change	- 1x3 = - 3 u	- 4x2 = - 8 u
After	2x3 = 6 u	3x2 = 6 u

Fraction of Vanessa's money left
= 1 - ¹₃
= ²₃

Fraction of Carl's money left
= 1 - ⁴₇
= ³₇

Carl and Vanessa had the same amount of money in the end. Make the numerators the same. LCM of 2 and 3 is 6.

²₃ of Vanessa's money = ³₇ of Carl's money
⁶₉ of Vanessa's money = ⁶₁₄ of Carl's money

Amount that Vanessa had at first = 9 u
Amount that Carl had at first = 14 u

Amount that Vanessa had less than Carl had at first
= 14 u - 9 u
= 5 u

5 u = 325

1 u = 325 ÷ 5 = 65

Amount that Carl had at first
= 14 u
= 14 x 65
= $910

Answer(s): $910