Jade had $416 less than Ben. Jade spent ¹₄ of her money and Ben spent ⁵₇ of his money. In the end, Ben and Jade had the same amount of money left. Find the amount of money Ben had at first.

	Jade	Ben	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 Jade's money left
= 1 - ¹₄
= ³₄

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

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

³₄ of Jade's money = ²₇ of Ben's money
⁶₈ of Jade's money = ⁶₂₁ of Ben's money

Amount that Jade had at first = 8 u
Amount that Ben had at first = 21 u

Amount that Jade had less than Ben had at first
= 21 u - 8 u
= 13 u

13 u = 416

1 u = 416 ÷ 13 = 32

Amount that Ben had at first
= 21 u
= 21 x 32
= $672

Answer(s): $672