Cathy had $494 less than Zeph. Cathy spent ¹₅ of her money and Zeph spent ⁴₇ of his money. In the end, Zeph and Cathy had the same amount of money left. Find the amount of money Zeph had at first.

	Cathy	Zeph	Difference
Before	5x3 = 15 u	7x4 = 28 u	13 u
Change	- 1x3 = - 3 u	- 4x4 = - 16 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of Cathy's money left
= 1 - ¹₅
= ⁴₅

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

Zeph and Cathy had the same amount of money in the end. Make the numerators the same. LCM of 4 and 3 is 12.

⁴₅ of Cathy's money = ³₇ of Zeph's money
¹²₁₅ of Cathy's money = ¹²₂₈ of Zeph's money

Amount that Cathy had at first = 15 u
Amount that Zeph had at first = 28 u

Amount that Cathy had less than Zeph had at first
= 28 u - 15 u
= 13 u

13 u = 494

1 u = 494 ÷ 13 = 38

Amount that Zeph had at first
= 28 u
= 28 x 38
= $1064

Answer(s): $1064