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Math Help - adding in squares

  1. #1
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    adding in squares

    I need help figuring out how to approach solving the attached problem and others like it. Single digit numbers are a piece of cake, no logic involved, but when the numbers become double digit you can spin your wheels filling in the squares. There has to be a trick to starting, any ideas????
    Attached Thumbnails Attached Thumbnails adding in squares-problem_2.gif  
    Last edited by Hunter385; September 28th 2008 at 09:30 AM.
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  2. #2
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    Hello, Hunter385!

    You said the first one was "a piece of cake".
    How did you solve it? . . . Trial and error?


    . . . \begin{array}{|c|c|}\hline a & b \\ \hline c & d \\ \hline \end{array}\begin{array}{c}38 \\ 64\end{array}
    . 49\;\;45\;\;57\;\; 53

    We have six equations:

    . . \begin{array}{cc}a+b\:=\:38 & [1] \\ c+d\:=\:64 & [2] \\ a+c \:=\:45 & [3] \\ b+d\:=\:57 & [4] \\ a+d\:=\:53 & [5] \\ b+c\:=\:49 & [6] \end{array}


    \begin{array}{cccccc}<br />
\text{Subtract [1] - [3]:} & b-c &=&\text{-}7  \\<br />
\text{Add [6]:} & b + c &=& 49 \end{array}

    And we have: . 2b \:= \:42\quad\Rightarrow\quad \boxed{b \:=\:21} \quad\Rightarrow\quad\boxed{ c \:=\:28}


    \begin{array}{cccccc}<br />
\text{Subtract [1] - [4]:} & a - d &=& \text{-}19 \\<br />
\text{Add [5]:} & a + d &=& 53 \end{array}

    And we have: . 2a \:=\:34\quad\Rightarrow\quad \boxed{a \:=\:17} \quad\Rightarrow\quad \boxed{d \:=\:36}


    . . . Solution: . \begin{array}{|c|c|}\hline 17 & 21 \\ \hline 28 & 36 \\ \hline \end{array}

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