Jane had $882 less than Dylan. Jane spent ¹₅ of her money and Dylan spent ⁵₇ of his money. In the end, Dylan and Jane had the same amount of money left. Find the amount of money Dylan had at first.

	Jane	Dylan	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 Jane's money left
= 1 - ¹₅
= ⁴₅

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

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

⁴₅ of Jane's money = ²₇ of Dylan's money
⁴₅ of Jane's money = ⁴₁₄ of Dylan's money

Amount that Jane had at first = 5 u
Amount that Dylan had at first = 14 u

Amount that Jane had less than Dylan had at first
= 14 u - 5 u
= 9 u

9 u = 882

1 u = 882 ÷ 9 = 98

Amount that Dylan had at first
= 14 u
= 14 x 98
= $1372

Answer(s): $1372