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Math Help - Word problem using linear equation...

  1. #1
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    Word problem using linear equation...

    "The sum of three numbers is 38. The second number is 2 more than three times the first number. The third number is equals half the difference between the first two numbers. What are the numbers?"

    Here's what I have so far:

    n = the first number
    3n+2 = the second number
    3n+2-n/2 = the third number

    Am I correct so far?
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  2. #2
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    Re: Word problem using linear equation...

    For 3rd number it is clearer to write (3n+2-n)/2=(2n+2)/2=n+1
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  3. #3
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    Re: Word problem using linear equation...

    I'm gonna ask a dumb question, but where does the n+1 come from?
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  4. #4
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    Re: Word problem using linear equation...

    \begin{cases}a+b+c=38 \\ b=3a+2 \\ c=\frac{b-a}{2}\end{cases}

    or

    \begin{cases}a+b+c=38 \\ b=3a+2 \\ c=\frac{a-b}{2}\end{cases}
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  5. #5
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    Re: Word problem using linear equation...

    Quote Originally Posted by Builderjay2011 View Post
    I'm gonna ask a dumb question, but where does the n+1 come from?
    (2n+2)/2=2(n+1)/2 Cancel the 2 and get (n+1)
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  6. #6
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    Re: Word problem using linear equation...

    So I should have the following:

    n+3n+2+(3n+2-n)/2=38
    2n+6n+4+3n+2-n=76
    10n+6=76
    10n=70
    n=7

    n=7 (first number)

    3(7)+2=23 (second number)

    23-7=16/2
    =8 (third number)

    7, 23, 8

    Hope that's right!
    Last edited by Builderjay2011; May 9th 2012 at 10:16 AM.
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  7. #7
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    Re: Word problem using linear equation...

    Correct.
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  8. #8
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    Re: Word problem using linear equation...

    "The sum of three numbers is 38. The second number is 2 more than three times the first number. The third number is equals half the difference between the first two numbers. What are the numbers?"
    As you say, calling the first number n, the second number is 3n+ 2 and the third number is ((3n+2)- n)/2= (2n+ 2)/2= 2(n+1)/2= n+ 1.

    But that does NOT tell you what the individual numbers are. If the first number is 1, then the second number is 5 and the third number is 3. If the second number is 2, the second number is 8 and the third number is 3. You can take any number to be the first number and then find values for the second number and third number.
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  9. #9
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    Re: Word problem using linear equation

    Quote Originally Posted by HallsofIvy View Post
    But that does NOT tell you what the individual numbers are. If the first number is 1, then the second number is 5 and the third number is 3. If the second number is 2, the second number is 8 and the third number is 3. You can take any number to be the first number and then find values for the second number and third number.
    It DOES tell you what the sum of the three numbers are though.
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  10. #10
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    Re: Word problem using linear equation...

    For some reason I just missed the that completely!
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