Yoko had $693 less than Ben. Yoko spent ¹₅ of her money and Ben spent ⁵₇ of his money. In the end, Ben and Yoko had the same amount of money left. Find the amount of money Ben had at first.

	Yoko	Ben	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 Yoko's money left
= 1 - ¹₅
= ⁴₅

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

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

⁴₅ of Yoko's money = ²₇ of Ben's money
⁴₅ of Yoko's money = ⁴₁₄ of Ben's money

Amount that Yoko had at first = 5 u
Amount that Ben had at first = 14 u

Amount that Yoko had less than Ben had at first
= 14 u - 5 u
= 9 u

9 u = 693

1 u = 693 ÷ 9 = 77

Amount that Ben had at first
= 14 u
= 14 x 77
= $1078

Answer(s): $1078