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Math Help - A tricky linear equation

  1. #1
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    Post A tricky linear equation

    If a and b are natural numbers and a + b + ab = 948 then find the value of a + b
    Please Help!
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  2. #2
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    Hello, anshulbshah!

    If a and b are natural numbers and a + b + ab \:=\: 948

    then find the value of a + b.

    Add 1 to both sides: . ab + a + b + 1 \:=\:949

    Factor both sides: . (a+1)(b+1) \:=\:13\cdot73

    One solution is: . \begin{array}{ccccc} a+1 \:=\:13 & \Rightarrow & a \:=\:12 \\ b+1 \:=\:73 & \Rightarrow & b \:=\:72 \end{array}


    Therefore: . a + b \;=\;12 + 72 \;=\;\boxed{84}

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