Usha had $735 less than Owen. Usha spent ¹₅ of her money and Owen spent ²₃ of his money. In the end, Owen and Usha had the same amount of money left. Find the amount of money Owen had at first.

	Usha	Owen	Difference
Before	5x1 = 5 u	3x4 = 12 u	7 u
Change	- 1x1 = - 1 u	- 2x4 = - 8 u
After	4x1 = 4 u	1x4 = 4 u

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

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

Owen and Usha had the same amount of money in the end. Make the numerators the same. LCM of 4 and 1 is 4.

⁴₅ of Usha's money = ¹₃ of Owen's money
⁴₅ of Usha's money = ⁴₁₂ of Owen's money

Amount that Usha had at first = 5 u
Amount that Owen had at first = 12 u

Amount that Usha had less than Owen had at first
= 12 u - 5 u
= 7 u

7 u = 735

1 u = 735 ÷ 7 = 105

Amount that Owen had at first
= 12 u
= 12 x 105
= $1260

Answer(s): $1260