Elyse had $210 less than Billy. Elyse spent ¹₄ of her money and Billy spent ²₃ of his money. In the end, Billy and Elyse had the same amount of money left. Find the amount of money Billy had at first.

	Elyse	Billy	Difference
Before	4x1 = 4 u	3x3 = 9 u	5 u
Change	- 1x1 = - 1 u	- 2x3 = - 6 u
After	3x1 = 3 u	1x3 = 3 u

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

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

Billy and Elyse had the same amount of money in the end. Make the numerators the same. LCM of 3 and 1 is 3.

³₄ of Elyse's money = ¹₃ of Billy's money
³₄ of Elyse's money = ³₉ of Billy's money

Amount that Elyse had at first = 4 u
Amount that Billy had at first = 9 u

Amount that Elyse had less than Billy had at first
= 9 u - 4 u
= 5 u

5 u = 210

1 u = 210 ÷ 5 = 42

Amount that Billy had at first
= 9 u
= 9 x 42
= $378

Answer(s): $378