Penelope had $420 less than George. Penelope spent ¹₇ of her money and George spent ⁴₇ of his money. In the end, George and Penelope had the same amount of money left. Find the amount of money George had at first.

	Penelope	George	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 Penelope's money left
= 1 - ¹₇
= ⁶₇

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

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

⁶₇ of Penelope's money = ³₇ of George's money
⁶₇ of Penelope's money = ⁶₁₄ of George's money

Amount that Penelope had at first = 7 u
Amount that George had at first = 14 u

Amount that Penelope had less than George had at first
= 14 u - 7 u
= 7 u

7 u = 420

1 u = 420 ÷ 7 = 60

Amount that George had at first
= 14 u
= 14 x 60
= $840

Answer(s): $840