Fanny had $279 less than Harry. Fanny spent ¹₆ of her money and Harry spent ²₃ of his money. In the end, Harry and Fanny had the same amount of money left. Find the amount of money Harry had at first.

	Fanny	Harry	Difference
Before	6x1 = 6 u	3x5 = 15 u	9 u
Change	- 1x1 = - 1 u	- 2x5 = - 10 u
After	5x1 = 5 u	1x5 = 5 u

Fraction of Fanny's money left
= 1 - ¹₆
= ⁵₆

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

Harry and Fanny had the same amount of money in the end. Make the numerators the same. LCM of 5 and 1 is 5.

⁵₆ of Fanny's money = ¹₃ of Harry's money
⁵₆ of Fanny's money = ⁵₁₅ of Harry's money

Amount that Fanny had at first = 6 u
Amount that Harry had at first = 15 u

Amount that Fanny had less than Harry had at first
= 15 u - 6 u
= 9 u

9 u = 279

1 u = 279 ÷ 9 = 31

Amount that Harry had at first
= 15 u
= 15 x 31
= $465

Answer(s): $465