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Thread: Discounted Price

  1. #1
    Super Member harpazo's Avatar
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    Discounted Price

    The price of a certain tv set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of

    A. 20 percent
    B. 19 percent
    C. 18 percent
    D. 11 percent
    E. 10 percent

    I decided to subtract 0.10 from 1. This led to 0.90.
    I then decided to subtract 0.10 from 0.90. This led to 0.80.
    I concluded that the answer must by 20 percent because 20 percent plus 80 percent is 100 percent.
    So, 1 - 0.20 = 0.80.

    The book's answer is B, however. My answer is A. Why is my answer wrong?
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  2. #2
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    Re: Discounted Price

    Let x = the original price of the TV set


    First discount: x - 0.1x = 1x - 0.1x = (1 - 0.1)x = 0.9x

    Second discount: 0.9x - 0.1(0.9x) = 0.9x - 0.09x = (0.9 - 0.09)x = 0.81x

    You're left with 81% of the original price.

    The equivalent single discount is (100%)x - (81%)x = (19%)x.


    B. 19 percent


    - - - - - - - - - - - - - - - - - - - - - OR - - - - - - - - - - - - - - - - - - - - - -


    (0.9x)(0.9) = 0.81x

    x - 0.81x = 1x - 0.81x = (1 - 0.81)x = 0.19x

    (19%)x


    B. 19 percent
    Last edited by greg1313; Feb 2nd 2019 at 06:45 AM.
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  3. #3
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    Re: Discounted Price

    Quote Originally Posted by harpazo View Post
    I then decided to subtract 0.10 from 0.90. This led to 0.80.

    The book's answer is B, however. My answer is A. Why is my answer wrong?
    100 - .10(100) = 90
    90 - .10(90) = 81

    Your way assumes a 20% discount right away...
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  4. #4
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    Re: Discounted Price

    Quote Originally Posted by harpazo View Post
    The price of a certain tv set is discounted by 10 percent, and the reduced price is then discounted by 10 percent. This series of successive discounts is equivalent to a single discount of

    A. 20 percent
    B. 19 percent
    C. 18 percent
    D. 11 percent
    E. 10 percent

    I decided to subtract 0.10 from 1. This led to 0.90.
    I then decided to subtract 0.10 from 0.90. This led to 0.80. This is where you have gone wrong. You should be subtracting 10% of 0.90 (which is 0.09 not 0.10) from 0.90.
    I concluded that the answer must by 20 percent because 20 percent plus 80 percent is 100 percent.
    So, 1 - 0.20 = 0.80.

    The book's answer is B, however. My answer is A. Why is my answer wrong?
    See comment in red.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Discounted Price

    Thank you everyone.
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