Jean had $455 less than Sean. Jean spent ¹₅ of her money and Sean spent ³₅ of his money. In the end, Sean and Jean had the same amount of money left. Find the amount of money Sean had at first.

	Jean	Sean	Difference
Before	5x1 = 5 u	5x2 = 10 u	5 u
Change	- 1x1 = - 1 u	- 3x2 = - 6 u
After	4x1 = 4 u	2x2 = 4 u

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

Fraction of Sean's money left
= 1 - ³₅
= ²₅

Sean and Jean had the same amount of money in the end. Make the numerators the same. LCM of 4 and 2 is 4.

⁴₅ of Jean's money = ²₅ of Sean's money
⁴₅ of Jean's money = ⁴₁₀ of Sean's money

Amount that Jean had at first = 5 u
Amount that Sean had at first = 10 u

Amount that Jean had less than Sean had at first
= 10 u - 5 u
= 5 u

5 u = 455

1 u = 455 ÷ 5 = 91

Amount that Sean had at first
= 10 u
= 10 x 91
= $910

Answer(s): $910