Gem had $147 less than Fabian. Gem spent ¹₇ of her money and Fabian spent ⁴₇ of his money. In the end, Fabian and Gem had the same amount of money left. Find the amount of money Fabian had at first.

	Gem	Fabian	Difference
Before	7x1 = 7 u	7x2 = 14 u	7 u
Change	- 1x1 = - 1 u	- 4x2 = - 8 u
After	6x1 = 6 u	3x2 = 6 u

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

Fraction of Fabian's money left
= 1 - ⁴₇
= ³₇

Fabian and Gem had the same amount of money in the end. Make the numerators the same. LCM of 6 and 3 is 6.

⁶₇ of Gem's money = ³₇ of Fabian's money
⁶₇ of Gem's money = ⁶₁₄ of Fabian's money

Amount that Gem had at first = 7 u
Amount that Fabian had at first = 14 u

Amount that Gem had less than Fabian had at first
= 14 u - 7 u
= 7 u

7 u = 147

1 u = 147 ÷ 7 = 21

Amount that Fabian had at first
= 14 u
= 14 x 21
= $294

Answer(s): $294