Q50. - Algebra 2

Question

For exercises 49 and 50, use the following information.

The U.S. Postal Service defines an oversized package as one for which the length $\mathbf{L}$ of its longest side plus the distance $\mathbf{D}$around its thickest part is more than 108 inches and less than or equal to 130 inches.

If the distance around the thickest part of a package you want to mail is 24 inches, describe the range of lengths that would classify your package as oversized.

Step-by-Step Solution

Answer

$\mathbf{84}<\mathbf{L}\le \mathbf{106}$

Step 1 &ndash; Description of step.

The length of the longest side of the package is $L$ and $D$ is the distance around the thickest part. According to the Postal Service oversized package is the one whose longest length plus thickest part distance is more than 108 inches and less than or equal to 130 inches.

Step 2 &ndash; Description of step.

Write an inequality to describe the given situation using the information in step 2.

 

$108<L+D\le 130$

Step 3 &ndash; Description of step.

The distance around the thickest part, that is, $D$ is $24$ inches.

 Subtract 24 from each side of the inequality and simplify.

$\begin{array}{c}108-24<L+24-24\le 130-24\\ 84<L\le 106\end{array}$

Therefore, the range of length to classify your package is $84<L\le 106$.