## Precalculus (6th Edition) Blitzer

The total area $A$ of the page as a function of the width $x$ is $A\left( x \right)=\frac{50}{x}+2x+52$.
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 $A\left( x \right)=\frac{50}{x}+2x+52$.