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Math Help - Find the Smallest Integer

  1. #1
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    Find the Smallest Integer

    The product of two integers is -24. If the same two integers are added, the sum is -23. Find the smallest of the two integers.

    This is what I did:

    x*y = -24......Equation A
    x + y = -23...Equation B

    I solved Equation B for y and got y = -x - 23.

    I plugged the value of y into Equation A for y and solved for x.

    x(-x - 23) = -24

    -x^2 - 23x = -24

    I moved everything to the right side.

    0 = x^2 + 23x - 24

    My final answer is -24 but the math book tells me that the answer is -23. Can you please explain who is right and why?



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  2. #2
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    Quote Originally Posted by sharkman View Post
    The product of two integers is -24. If the same two integers are added, the sum is -23. Find the smallest of the two integers.

    This is what I did:

    x*y = -24......Equation A
    x + y = -23...Equation B

    I solved Equation B for y and got y = -x - 23.

    I plugged the value of y into Equation A for y and solved for x.

    x(-x - 23) = -24

    -x^2 - 23x = -24

    I moved everything to the right side.

    0 = x^2 + 23x - 24

    My final answer is -24 but the math book tells me that the answer is -23. Can you please explain who is right and why?
    You are right, because (-24)*(1) = -24 and (-24) + 1 = -23... just like the statement of the problem demands.
    -23 does not satisfy given conditions.
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  3. #3
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    I knew it!

    Quote Originally Posted by Isomorphism View Post
    You are right, because (-24)*(1) = -24 and (-24) + 1 = -23... just like the statement of the problem demands.
    -23 does not satisfy given conditions.
    I better get a new math book. Why do so many books have errors in the answer section?
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