Linda had $294 less than Liam. Linda spent ¹₇ of her money and Liam spent ⁵₇ of his money. In the end, Liam and Linda had the same amount of money left. Find the amount of money Liam had at first.

	Linda	Liam	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 Linda's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Linda's money = ²₇ of Liam's money
⁶₇ of Linda's money = ⁶₂₁ of Liam's money

Amount that Linda had at first = 7 u
Amount that Liam had at first = 21 u

Amount that Linda had less than Liam had at first
= 21 u - 7 u
= 14 u

14 u = 294

1 u = 294 ÷ 14 = 21

Amount that Liam had at first
= 21 u
= 21 x 21
= $441

Answer(s): $441