Emily had $360 less than Tim. Emily spent ¹₆ of her money and Tim spent ²₃ of his money. In the end, Tim and Emily had the same amount of money left. Find the amount of money Tim had at first.

	Emily	Tim	Difference
Before	6x1 = 6 u	3x5 = 15 u	9 u
Change	- 1x1 = - 1 u	- 2x5 = - 10 u
After	5x1 = 5 u	1x5 = 5 u

Fraction of Emily's money left
= 1 - ¹₆
= ⁵₆

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

Tim and Emily had the same amount of money in the end. Make the numerators the same. LCM of 5 and 1 is 5.

⁵₆ of Emily's money = ¹₃ of Tim's money
⁵₆ of Emily's money = ⁵₁₅ of Tim's money

Amount that Emily had at first = 6 u
Amount that Tim had at first = 15 u

Amount that Emily had less than Tim had at first
= 15 u - 6 u
= 9 u

9 u = 360

1 u = 360 ÷ 9 = 40

Amount that Tim had at first
= 15 u
= 15 x 40
= $600

Answer(s): $600