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Question 458160: 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 for the same amount. How many shares did he buy?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! 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
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since x*p = 2000
x = 2000/p
p = 2000/x
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(x+10)(p-10) = 2000
xp -10x +10p -100 = 2000
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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 <
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(p-50)(p+40) = 0
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p = 50 or -40, but a negative stock price is nonsense.
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p = 50
x = 2000/p
x = 40
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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 is 10 more shares than he bought the first week.
.
Done.
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