Sarah had $256 less than Howard. Sarah spent ¹₇ of her money and Howard spent ³₅ of his money. In the end, Howard and Sarah had the same amount of money left. Find the amount of money Howard had at first.

	Sarah	Howard	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

Fraction of Sarah's money left
= 1 - ¹₇
= ⁶₇

Fraction of Howard's money left
= 1 - ³₅
= ²₅

Howard and Sarah had the same amount of money in the end. Make the numerators the same. LCM of 6 and 2 is 6.

⁶₇ of Sarah's money = ²₅ of Howard's money
⁶₇ of Sarah's money = ⁶₁₅ of Howard's money

Amount that Sarah had at first = 7 u
Amount that Howard had at first = 15 u

Amount that Sarah had less than Howard had at first
= 15 u - 7 u
= 8 u

8 u = 256

1 u = 256 ÷ 8 = 32

Amount that Howard had at first
= 15 u
= 15 x 32
= $480

Answer(s): $480