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Math Help - Problem solving question

  1. #1
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    Problem solving question

    Hi guys, I am at a loss when it comes to these questions, so I was wondering if somebody would help me out.

    Identify the numbers represented by letters.
    P, Q, R are all different numbers and not zero.
    QP0 x
    PQR
    3RR0 +
    49Q00
    QP000
    P242R0
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Re: Problem solving question

    Hello, HerroDere!

    This is called an "Alphametic".


    \text{Identify the digits represented by letters. }\;P, Q, R\text{ are different nonzero digits.}

    . . \begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& Q & P & 0 \\ && \times & P & Q & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & Q & 0 \\ & Q & P & 0 \\ \hline P & 2 & 4 & 2 & R & 0 \end{array}

    In column-1, we see that P = 1.


    \text{We have: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& Q & 1 & 0 \\ && \times & 1 & Q & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & Q & 0 \\ & Q & 1 & 0 \\ \hline 1 & 2 & 4 & 2 & R & 0 \end{array}



    In column-3, we see that the sum is 14.
    Hence, column-2 is: . 4 + Q + 1 \:=\:12 \quad\Rightarrow\quad Q = 7


    \text{We have: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& 7 & 1 & 0 \\ && \times & 1 & 7 & R \\ \hline && 3 & R & R & 0 \\ & 4 & 9 & 7 & 0 \\ & 7 & 1 & 0 \\ \hline 1 & 2 & 4 & 2 & R & 0 \end{array}



    In column-4: . R + 7 \,=\,12 \quad\Rightarrow\quad R \,=\,5


    \text{Therefore: }\;\begin{array}{ccccccc} ^1 & ^2 & ^3 & ^4 & ^5 & ^6 \\ &&& 7 & 1 & 0 \\ && \times & 1 & 7 & 5 \\ \hline && 3 & 5 & 5 & 0 \\ & 4 & 9 & 7 & 0 \\ & 7 & 1 & 0 \\ \hline 1 & 2 & 4 & 2 &7 & 0 \end{array}
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  3. #3
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    Re: Problem solving question

    thanks for that your explanation really helped
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