Linda had $351 less than Julian. Linda spent ¹₅ of her money and Julian spent ⁵₇ of his money. In the end, Julian and Linda had the same amount of money left. Find the amount of money Julian had at first.

	Linda	Julian	Difference
Before	5x1 = 5 u	7x2 = 14 u	9 u
Change	- 1x1 = - 1 u	- 5x2 = - 10 u
After	4x1 = 4 u	2x2 = 4 u

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

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

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

⁴₅ of Linda's money = ²₇ of Julian's money
⁴₅ of Linda's money = ⁴₁₄ of Julian's money

Amount that Linda had at first = 5 u
Amount that Julian had at first = 14 u

Amount that Linda had less than Julian had at first
= 14 u - 5 u
= 9 u

9 u = 351

1 u = 351 ÷ 9 = 39

Amount that Julian had at first
= 14 u
= 14 x 39
= $546

Answer(s): $546