# Math Help - A tricky linear equation

1. ## A tricky linear equation

If a and b are natural numbers and a + b + ab = 948 then find the value of a + b

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