Roshel had $1118 less than Luke. Roshel spent ¹₄ of her money and Luke spent ⁵₇ of his money. In the end, Luke and Roshel had the same amount of money left. Find the amount of money Luke had at first.

	Roshel	Luke	Difference
Before	4x2 = 8 u	7x3 = 21 u	13 u
Change	- 1x2 = - 2 u	- 5x3 = - 15 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of Roshel's money left
= 1 - ¹₄
= ³₄

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

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

³₄ of Roshel's money = ²₇ of Luke's money
⁶₈ of Roshel's money = ⁶₂₁ of Luke's money

Amount that Roshel had at first = 8 u
Amount that Luke had at first = 21 u

Amount that Roshel had less than Luke had at first
= 21 u - 8 u
= 13 u

13 u = 1118

1 u = 1118 ÷ 13 = 86

Amount that Luke had at first
= 21 u
= 21 x 86
= $1806

Answer(s): $1806