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Math Help - Difficulty with a math word problem. Help me out here please.

  1. #1
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    Difficulty with a math word problem. Help me out here please.

    Ok, I'm getting ready to go to school this summer, and in the meantime, I'm trying to learn as much as I can in regards to math (since physics is going to be my major). At this point, I've been working on a book that goes over math word problems, and I have gotten hung-up on just one problem in the book that I can't figure out.

    Here is the word problem:

    "In a two-digit number, the ten's digit is 3 more than the one's digit. If the digit's are reversed, the difference between the two numbers is 27. Find the number."

    Now, here's how I went about trying to solve this:

    x = first number (one's digit)
    x+3 = second number (ten's digit)

    Then, to account for placing the first and second numbers in the tenth's place for regular and reverse, I tried this equation:

    10(x+3)+x=10x+x+3+27

    The first equation before the equals is the original number, the second one is reversing the numbers, then I added 27 to compensate for the difference that is supposed to be between them. However, when I set the equation up like this, all the "x"s end up cancelling themselves out, like so.

    10x+30+x=11x+30
    11x+30=11x+30

    Hence, I end up cancelling it all out. Since the book I am studying from doesn't explain the exact formula when you are using the "difference" between the two numbers, I'm not sure how else to do this.

    I also tried this equation, but I still end up cancelling out the x's:

    10(x+3)+x-(10x+x+3)=27
    10x+30+x-10x-x-3=27
    11x+30-11x-3=27
    11x-11x+27=27

    Can someone please tell me what I'm doing wrong here and the correct way to solve for "x", hence solving for the two digits?
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  2. #2
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    Crna Gora
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    Re: Difficulty with a math word problem. Help me out here please.

    \begin{cases}x=3+y \\\overline{xy}-\overline{yx}=27\end{cases}

    hence :

    \begin{cases}x=3+y \\10x+y-(10y+x)=27\end{cases}

    This system is undetermined so solutions are :

    \overline{xy} \in \{30,41,52,63,74,85,96\}
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  3. #3
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    Bartow, FL
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    Re: Difficulty with a math word problem. Help me out here please.

    Quote Originally Posted by princeps View Post
    \begin{cases}x=3+y \\\overline{xy}-\overline{yx}=27\end{cases}

    hence :

    \begin{cases}x=3+y \\10x+y-(10y+x)=27\end{cases}

    This system is undetermined so solutions are :

    \overline{xy} \in \{30,41,52,63,74,85,96\}
    Thanks for the help here. Your method is much different than the one explained in the book, but the book also laid it out as if there was only one correct answer. Funny thing is, 3 out of the 4 multiple-choice they let you choose from are correct. I knew something wasn't right when I tried plugging in two different answers and both seemed correct.

    Anyway, guess there is a lot more that I need to learn here, and that the book I am reading now (Math Word Problems Demystified) doesn't give the optimal methods to solve the word problems. Well, thanks again.
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