Yoko had $494 less than Tim. Yoko spent ¹₄ of her money and Tim spent ⁵₇ of his money. In the end, Tim and Yoko had the same amount of money left. Find the amount of money Tim had at first.

	Yoko	Tim	Difference
Before	4x2 = 8 u	7x3 = 21 u	13 u
Change	- 1x2 = - 2 u	- 5x3 = - 15 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of Yoko's money left
= 1 - ¹₄
= ³₄

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

Tim and Yoko had the same amount of money in the end. Make the numerators the same. LCM of 3 and 2 is 6.

³₄ of Yoko's money = ²₇ of Tim's money
⁶₈ of Yoko's money = ⁶₂₁ of Tim's money

Amount that Yoko had at first = 8 u
Amount that Tim had at first = 21 u

Amount that Yoko had less than Tim had at first
= 21 u - 8 u
= 13 u

13 u = 494

1 u = 494 ÷ 13 = 38

Amount that Tim had at first
= 21 u
= 21 x 38
= $798

Answer(s): $798