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23 November, 13:40

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

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Answers (1)
  1. 23 November, 15:41
    0
    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!
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