Olivia had $824 less than Julian. Olivia spent ¹₇ of her money and Julian spent ³₅ of his money. In the end, Julian and Olivia had the same amount of money left. Find the amount of money Julian had at first.

	Olivia	Julian	Difference
Before	7x1 = 7 u	5x3 = 15 u	8 u
Change	- 1x1 = - 1 u	- 3x3 = - 9 u
After	6x1 = 6 u	2x3 = 6 u

Fraction of Olivia's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Olivia's money = ²₅ of Julian's money
⁶₇ of Olivia's money = ⁶₁₅ of Julian's money

Amount that Olivia had at first = 7 u
Amount that Julian had at first = 15 u

Amount that Olivia had less than Julian had at first
= 15 u - 7 u
= 8 u

8 u = 824

1 u = 824 ÷ 8 = 103

Amount that Julian had at first
= 15 u
= 15 x 103
= $1545

Answer(s): $1545