If a and b are natural numbers and a + b + ab = 948 then find the value of a + b
Please Help!
Hello, anshulbshah!
If $\displaystyle a$ and $\displaystyle b$ are natural numbers and $\displaystyle a + b + ab \:=\: 948$
then find the value of $\displaystyle a + b$.
Add 1 to both sides: .$\displaystyle ab + a + b + 1 \:=\:949$
Factor both sides: .$\displaystyle (a+1)(b+1) \:=\:13\cdot73$
One solution is: .$\displaystyle \begin{array}{ccccc} a+1 \:=\:13 & \Rightarrow & a \:=\:12 \\ b+1 \:=\:73 & \Rightarrow & b \:=\:72 \end{array}$
Therefore: .$\displaystyle a + b \;=\;12 + 72 \;=\;\boxed{84}$