Sarah had $819 less than Billy. Sarah spent ¹₅ of her money and Billy spent ⁴₇ of his money. In the end, Billy and Sarah had the same amount of money left. Find the amount of money Billy had at first.

	Sarah	Billy	Difference
Before	5x3 = 15 u	7x4 = 28 u	13 u
Change	- 1x3 = - 3 u	- 4x4 = - 16 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of Sarah's money left
= 1 - ¹₅
= ⁴₅

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

Billy and Sarah had the same amount of money in the end. Make the numerators the same. LCM of 4 and 3 is 12.

⁴₅ of Sarah's money = ³₇ of Billy's money
¹²₁₅ of Sarah's money = ¹²₂₈ of Billy's money

Amount that Sarah had at first = 15 u
Amount that Billy had at first = 28 u

Amount that Sarah had less than Billy had at first
= 28 u - 15 u
= 13 u

13 u = 819

1 u = 819 ÷ 13 = 63

Amount that Billy had at first
= 28 u
= 28 x 63
= $1764

Answer(s): $1764