Question

The length of a rectangle should be 15 meters longer than 5 times the width. If the length must be between40 and 80 meters long, what are the restrictions for the width, y?Write the solution set as an algebraic inequality solved for the variable.

Answer 1

Let l be length and width be w

The length of a rectangle should be 15 meters longer than 5 times the width:

$l=15+5w$

Length between 40 and 80, so:

$\begin{gathered} l=15+5w \\ 40=15+5w \\ 5w=25 \\ w=\frac{25}{5} \\ w=5 \end{gathered}$

and

$\begin{gathered} l=15+5w \\ 80=15+5w \\ 5w=65 \\ w=\frac{65}{5} \\ w=13 \end{gathered}$

Width in between 5 and 13.

$5\leq y\leq13$