Q1. - Algebra 1

Question

A shipping company charges $\mathrm{\backslash (}8.50$ to ship packages that weigh up to 1 pound and $\mathrm{\backslash )}7.25$ for each additional pound. Which of the following piecewise-defined functions represents the cost C of shipping a package that weighs p pounds?  

A $C\left(p\right)=\left\{\begin{array}{l}8.50\text{ if }p\le 1\\ 8.50+7.25p\text{ if }p>1\end{array}\right.$

B $C\left(p\right)=\left\{\begin{array}{l}7.25\text{ if }p\le 1\\ 7.25+8.50p\text{ if }p>1\end{array}\right.$

 

C $C\left(p\right)=\left\{\begin{array}{l}\text{8.50 if }p\le 1\\ 8.50p+7.25\left(p-1\right)\text{ if }p>1\end{array}\right.$

 

D $C\left(p\right)=\left\{\begin{array}{l}\text{8.50 if }p\le 1\\ 8.50+7.25\left(p-1\right)\text{ if }p>1\end{array}\right.$

Step-by-Step Solution

Answer

The correct equation is represented by A.  

Step 1. Determine the formula that can be used.

The standard form associated with the slope and the intercept form related to the line that is straight $y=mx+c$ in which the slope is represented by $m$ and the $y$-intercept is represented by $c$ can be used to write the required equation.

Step 2. Take the help of the obtained method.

Take the help of obtained standard form represented by $y=mx+c$ in which the required values can be filled by using the provided notations and the slope which is in the form of the additional pound and $y$-intercept which is in the form of the prize associated with the shipping having the weight of a single pound.

$C\left(p\right)=8.50+7.25p$

Step 3. Write the conclusion.

The obtained equation is $C\left(p\right)=8.50+7.25p$ so its function will be $C\left(p\right)=\left\{\begin{array}{l}8.50\text{ if }p\le 1\\ 8.50+7.25p\text{ if }p>1\end{array}\right.$ and it is the same as in option A.