Question

Ed bought $2,000 in stock shares one week before the stock price dropped $10.00. If he had waited for the price setback, he could have bought 10 more shares f or the same amount. How many shares did he buy?

1.)40
2.)50
3.)60

Answer 1

Answer: 40 shares is the correct answer.

Answer 2

The Answer is 1: 40 Shares

Proof:
In week 1, Ed purchased stock:
x = number of shares of stock he bought
p = purchase price per share
xp = 2000
One week later...the stock tumbled.
Price is now (p-10)
He could have bought 10 more shares: (x+10) for the same purchase price
(x+10)(p-10)=2000
since x*p = 2000
x = 2000/p
p = 2000/x
(x+10)(p-10) = 2000
xp -10x +10p -100 = 2000
substitute for x
(2000/p)*p - 10*(2000/p) +10p -100 = 2000
2000 -20000/p +10p -100 = 2000
-20000/p +10p = 100
multiply by p
-20000 + 10p^2 = 100p
10p^2 -100p - 20000 = 0
divide by 10
p^2 -10p - 2000 = 0
factor
20*100 = 2000 < 40*50 = 2000 < .
(p-50)(p+40) = 0
p = 50 or -40, but a negative stock price is nonsense.
p = 50
x = 2000/p
x = 40
So, in week 1, Ed purchased 40 shares at $50 per share.
The next week the stock fell by $10
Now the price is $40.
For $2000 he could buy 50 shares now.
Which are 10 more shares than he bought the first week!