Mary had $558 less than Owen. Mary spent ¹₆ of her money and Owen spent ²₃ of his money. In the end, Owen and Mary had the same amount of money left. Find the amount of money Owen had at first.

	Mary	Owen	Difference
Before	6x1 = 6 u	3x5 = 15 u	9 u
Change	- 1x1 = - 1 u	- 2x5 = - 10 u
After	5x1 = 5 u	1x5 = 5 u

Fraction of Mary's money left
= 1 - ¹₆
= ⁵₆

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

Owen and Mary had the same amount of money in the end. Make the numerators the same. LCM of 5 and 1 is 5.

⁵₆ of Mary's money = ¹₃ of Owen's money
⁵₆ of Mary's money = ⁵₁₅ of Owen's money

Amount that Mary had at first = 6 u
Amount that Owen had at first = 15 u

Amount that Mary had less than Owen had at first
= 15 u - 6 u
= 9 u

9 u = 558

1 u = 558 ÷ 9 = 62

Amount that Owen had at first
= 15 u
= 15 x 62
= $930

Answer(s): $930