Nicole had $806 less than Howard. Nicole spent ¹₄ of her money and Howard spent ⁵₇ of his money. In the end, Howard and Nicole had the same amount of money left. Find the amount of money Howard had at first.

	Nicole	Howard	Difference
Before	4x2 = 8 u	7x3 = 21 u	13 u
Change	- 1x2 = - 2 u	- 5x3 = - 15 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of Nicole's money left
= 1 - ¹₄
= ³₄

Fraction of Howard's money left
= 1 - ⁵₇
= ²₇

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

³₄ of Nicole's money = ²₇ of Howard's money
⁶₈ of Nicole's money = ⁶₂₁ of Howard's money

Amount that Nicole had at first = 8 u
Amount that Howard had at first = 21 u

Amount that Nicole had less than Howard had at first
= 21 u - 8 u
= 13 u

13 u = 806

1 u = 806 ÷ 13 = 62

Amount that Howard had at first
= 21 u
= 21 x 62
= $1302

Answer(s): $1302