College Algebra, Chapter 1, 1.2, Section 1.2, Problem 42

Suppose that a poster has a rectangular printed area 100 cm by 140 cm and a strip of uniform width around the edges. The perimeter of the poster is $\displaystyle 1 \frac{1}{2}$ times the perimeter of the printed area. What is the width of the strips?







Let $P_1$ and $P_2$ be the perimeter of the poster and printed area respectively. So..


$
\begin{equation}
\begin{aligned}

P_1 =& 2 (100 + 2x) + 2 (140 + 2x) \text{ and }
\\
\\
P_2 =& 2(100) + 2(140) = 480 \text{ cm}


\end{aligned}
\end{equation}
$


If we perform the condition,


$
\begin{equation}
\begin{aligned}

& P = 1 \frac{1}{2} P_2
&& \text{Model}
\\
\\
& 2(100 + 2x) + 2(140 + 2x) = \frac{3}{2} (480)
&& \text{Substitute the values and apply Distributive Property}
\\
\\
& 200 + 4x + 240 + 4x = 720
&& \text{Combine like terms and simplify}
\\
\\
& 8x = 720 - 440
&& \text{Solve for } x
\\
\\
& x = 35 \text{ cm}

\end{aligned}
\end{equation}
$