Answer
The total area $A$ of the page as a function of the width $x$ is $A\left( x \right)=\frac{50}{x}+2x+52$.
Work Step by Step
Consider the length and width of the printed page to be $y$ and $x$.
The printed area $a$ of the page is $50$ square feet.
Substitute $a=50$ in the formula $a=xy$.
$\begin{align}
& 50=xy \\
& \frac{50}{x}=y
\end{align}$
Consider the length and width of the page to be $l$ and $w$.
The length of the rectangular page is,
$\begin{align}
& l=y+1+1 \\
& l=y+2
\end{align}$
Substitute $y=\frac{50}{x}$ in the formula $l=y+2$.
$l=\frac{50}{x}+2$
The width of the rectangular page is,
$\begin{align}
& w=x+\frac{1}{2}+\frac{1}{2} \\
& w=x+1 \\
\end{align}$
The area of the rectangular page is expressed as $A$.
Substitute $l=\frac{50}{x}+2$ and $w=x+1$ in the equation $A=xy$.
$A=\left( \frac{50}{x}+2 \right)\left( x+1 \right)$
Use the distributive property.
$\begin{align}
& A=\frac{50}{x}\cdot x+\frac{50}{x}+2x+2 \\
& =50+\frac{50}{x}+2x+2 \\
& =\frac{50}{x}+2x+52
\end{align}$
Therefore, the total area $A$ of the page as a function of the width $x$ is $A\left( x \right)=\frac{50}{x}+2x+52$.
