Kimberly had $756 less than Tim. Kimberly spent ¹₅ of her money and Tim spent ²₃ of his money. In the end, Tim and Kimberly had the same amount of money left. Find the amount of money Tim had at first.

	Kimberly	Tim	Difference
Before	5x1 = 5 u	3x4 = 12 u	7 u
Change	- 1x1 = - 1 u	- 2x4 = - 8 u
After	4x1 = 4 u	1x4 = 4 u

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

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

Tim and Kimberly had the same amount of money in the end. Make the numerators the same. LCM of 4 and 1 is 4.

⁴₅ of Kimberly's money = ¹₃ of Tim's money
⁴₅ of Kimberly's money = ⁴₁₂ of Tim's money

Amount that Kimberly had at first = 5 u
Amount that Tim had at first = 12 u

Amount that Kimberly had less than Tim had at first
= 12 u - 5 u
= 7 u

7 u = 756

1 u = 756 ÷ 7 = 108

Amount that Tim had at first
= 12 u
= 12 x 108
= $1296

Answer(s): $1296