Fanny had $825 less than Tim. Fanny spent ¹₇ of her money and Tim spent ²₃ of his money. In the end, Tim and Fanny had the same amount of money left. Find the amount of money Tim had at first.

	Fanny	Tim	Difference
Before	7x1 = 7 u	3x6 = 18 u	11 u
Change	- 1x1 = - 1 u	- 2x6 = - 12 u
After	6x1 = 6 u	1x6 = 6 u

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

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

Tim and Fanny had the same amount of money in the end. Make the numerators the same. LCM of 6 and 1 is 6.

⁶₇ of Fanny's money = ¹₃ of Tim's money
⁶₇ of Fanny's money = ⁶₁₈ of Tim's money

Amount that Fanny had at first = 7 u
Amount that Tim had at first = 18 u

Amount that Fanny had less than Tim had at first
= 18 u - 7 u
= 11 u

11 u = 825

1 u = 825 ÷ 11 = 75

Amount that Tim had at first
= 18 u
= 18 x 75
= $1350

Answer(s): $1350