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Math Help - Find the Larger Integer

  1. #1
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    Find the Larger Integer

    The product of two integers is -40. If the same two integers are added, their sum is -3. Find the larger of the integers.

    I did this:

    x*y = -40...Equation A
    x + y = -3..Equation B

    I solved Equation B for y and got y = -x - 3.

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

    x(-x - 3) = -3

    -x^2 - 3x = -3

    I moved everything to the right side.

    0 = x^2 + 3x - 40

    My final answer is 5 but the math book tells me that the correct answer is -8. Can you explain who is right and why?

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  2. #2
    Super Member Matt Westwood's Avatar
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    Depends on whether they mean "largest" in the sense of "absolute value" (in which case it's -8) or "largest" in the sense of "most positive". Go back thru the book and see how they define "largest".
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  3. #3
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    Quote Originally Posted by sharkman View Post
    The product of two integers is -40. If the same two integers are added, their sum is -3. Find the larger of the integers.

    I did this:

    x*y = -40...Equation A
    x + y = -3..Equation B

    I solved Equation B for y and got y = -x - 3.

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

    x(-x - 3) = -40

    -x^2 - 3x = -3

    I moved everything to the right side.

    0 = x^2 + 3x - 40

    My final answer is 5 but the math book tells me that the correct answer is -8. Can you explain who is right and why?
    Note the minor correction above.
    But, yes you are correct.

    EDIT: I think that "largest" means largest.
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  4. #4
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    ok but...

    Quote Originally Posted by Plato View Post
    Note the minor correction above.
    But, yes you are correct.

    EDIT: I think that "largest" means largest.
    Are you saying that the equation x(-x - 3) = -40should not be equated to -40? But the question stated that the product of two integers is -40. I moved everything to the right side and so -40 remains -40, right? Please, explain what you meant by "minor correction" in your reply. Thank you.
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  5. #5
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    Quote Originally Posted by sharkman View Post
    Are you saying that the equation x(-x - 3) = -40should not be equated to -40? But the question stated that the product of two integers is -40. I moved everything to the right side and so -40 remains -40, right? Please, explain what you meant by "minor correction" in your reply. Thank you.
    Look at your OP.
    You had \color{red}x(-x-3)=-3.
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  6. #6
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    ok...

    Quote Originally Posted by Plato View Post
    Look at your OP.
    You had \color{red}x(-x-3)=-3.
    I finally see the typo. Thank you.
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