Sarah had $451 less than Flynn. Sarah spent ¹₇ of her money and Flynn spent ²₃ of his money. In the end, Flynn and Sarah had the same amount of money left. Find the amount of money Flynn had at first.

	Sarah	Flynn	Difference
Before	7x1 = 7 u	3x6 = 18 u	11 u
Change	- 1x1 = - 1 u	- 2x6 = - 12 u
After	6x1 = 6 u	1x6 = 6 u

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

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

Flynn and Sarah had the same amount of money in the end. Make the numerators the same. LCM of 6 and 1 is 6.

⁶₇ of Sarah's money = ¹₃ of Flynn's money
⁶₇ of Sarah's money = ⁶₁₈ of Flynn's money

Amount that Sarah had at first = 7 u
Amount that Flynn had at first = 18 u

Amount that Sarah had less than Flynn had at first
= 18 u - 7 u
= 11 u

11 u = 451

1 u = 451 ÷ 11 = 41

Amount that Flynn had at first
= 18 u
= 18 x 41
= $738

Answer(s): $738