Tiffany had $322 less than Billy. Tiffany spent ¹₇ of her money and Billy spent ⁵₇ of his money. In the end, Billy and Tiffany had the same amount of money left. Find the amount of money Billy had at first.

	Tiffany	Billy	Difference
Before	7x1 = 7 u	7x3 = 21 u	14 u
Change	- 1x1 = - 1 u	- 5x3 = - 15 u
After	6x1 = 6 u	2x3 = 6 u

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

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

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

⁶₇ of Tiffany's money = ²₇ of Billy's money
⁶₇ of Tiffany's money = ⁶₂₁ of Billy's money

Amount that Tiffany had at first = 7 u
Amount that Billy had at first = 21 u

Amount that Tiffany had less than Billy had at first
= 21 u - 7 u
= 14 u

14 u = 322

1 u = 322 ÷ 14 = 23

Amount that Billy had at first
= 21 u
= 21 x 23
= $483

Answer(s): $483