Fanny had $285 less than Billy. Fanny spent ¹₃ of her money and Billy spent ⁴₇ of his money. In the end, Billy and Fanny had the same amount of money left. Find the amount of money Billy had at first.

	Fanny	Billy	Difference
Before	3x3 = 9 u	7x2 = 14 u	5 u
Change	- 1x3 = - 3 u	- 4x2 = - 8 u
After	2x3 = 6 u	3x2 = 6 u

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

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

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

²₃ of Fanny's money = ³₇ of Billy's money
⁶₉ of Fanny's money = ⁶₁₄ of Billy's money

Amount that Fanny had at first = 9 u
Amount that Billy had at first = 14 u

Amount that Fanny had less than Billy had at first
= 14 u - 9 u
= 5 u

5 u = 285

1 u = 285 ÷ 5 = 57

Amount that Billy had at first
= 14 u
= 14 x 57
= $798

Answer(s): $798