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Math Help - By using algebraic method, find the value of the smallest value

  1. #1
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    By using algebraic method, find the value of the smallest value

    Question:
    The subtraction of two positive numbers is 4. When the two numbers are multiplied together, the resulting value is 21. By using algebraic method, find the value of the smallest number

    My workings:
    let x be the smallest number
    let x+4 be the bigger number
    (x+4)-x=4
    (x+4) x x=21
    x+4=4+x
    (x^2+4x)/4 = 21/4
    4(x^2+4x)=84
    4x^2+16x=84
    4x^2+16x-84=0
    (x+7) or (4x-12)
    x+7=0 or 4x-12=0
    x=-7 (N.A.) or 4x-12=0
    Therefore, x=3

    Am I right?

    Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: By using algebraic method, find the value of the smallest value

    Quote Originally Posted by FailInMaths View Post
    Question:
    The subtraction of two positive numbers is 4. When the two numbers are multiplied together, the resulting value is 21. By using algebraic method, find the value of the smallest number

    My workings:
    let x be the smallest number
    let x+4 be the bigger number
    (x+4)-x=4
    (x+4) x x=21
    x+4=4+x
    (x^2+4x)/4 = 21/4
    4(x^2+4x)=84
    4x^2+16x=84
    4x^2+16x-84=0
    (x+7) or (4x-12)
    x+7=0 or 4x-12=0
    x=-7 (N.A.) or 4x-12=0
    Therefore, x=3

    Am I right?

    Thanks
    Plug your numbers into the original equations and see if it works.
    Given that your smaller number is 3 then your larger number is 7.

    7 - 3 = 4 \text{ and  } 7 \times 3 = 21

    Since that is true and matches the question statement your answer is correct.


    Your working confused me though, why didn't you just go from saying x(x+4) = 21 in the second line to x^2+4x = 21 and then x^2+4x-21=0 and solve that quadratic?
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  3. #3
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    Re: By using algebraic method, find the value of the smallest value

    Quote Originally Posted by e^(i*pi) View Post
    Plug your numbers into the original equations and see if it works.
    Given that your smaller number is 3 then your larger number is 7.

    7 - 3 = 4 \text{ and  } 7 \times 3 = 21

    Since that is true and matches the question statement your answer is correct.


    Your working confused me though, why didn't you just go from saying x(x+4) = 21 in the second line to x^2+4x = 21 and then x^2+4x-21=0 and solve that quadratic?
    Oh, now that you say it. To be honest, I had been thinking for a few hours, so I am not really sure of what I am writing, thus want to have it checked here

    Thanks for spotting the mistake, I will amend it.

    Thanks
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