Chapter 1.1, Problem 26PPE

To determine

Model the relationship in the table.

Answer to Problem 26PPE

  $\$150+\left(\$2\times n\right)$

Explanation of Solution

Given information:

A salesperson at a shoe store earns a weekly salary of $\$150$ . A salesperson is also paid $\$2.00$ for each pair of shoes he or she sells during the week.

  

Calculation:

Here, we will consider the following table:

  $\begin{array}{ll}Pairsofshoessold\hfill & Totalearned\hfill \\ 5\hfill & \$150+\left(\$2\times 5\right)\hfill \\ 10\hfill & \$150+\left(\$2\times 10\right)\hfill \\ 15\hfill & \$150+\left(\$2\times 15\right)\hfill \\ n\hfill & \mathrm{.....}\hfill \end{array}$

Now, from the above table we can conclude that:

When he or she sold $5$ pair of shoes, the total earned will become:

  $\begin{array}{l}weeklysalary+\left(\begin{array}{l}extraamountheorshepaidforsellingnumberof\\ pairsofshoes\times numberofpairofshoes\end{array}\right)\\ wherenumberofpairofshoessold=5\end{array}$

When he or she sold $10$ pair of shoes, the total earned will become:

  $\begin{array}{l}weeklysalary+\left(\begin{array}{l}extraamountheorshepaidforsellingnumberof\\ pairsofshoes\times numberofpairofshoes\end{array}\right)\\ wherenumberofpairofshoessold=10\end{array}$

When he or she sold $15$ pair of shoes, the total earned will become:

  $\begin{array}{l}weeklysalary+\left(\begin{array}{l}extraamountheorshepaidforsellingnumberof\\ pairsofshoes\times numberofpairofshoes\end{array}\right)\\ wherenumberofpairofshoessold=15\end{array}$

When he or she sold $n$ pair of shoes, the total earned will become:

  $\begin{array}{l}weeklysalary+\left(\begin{array}{l}extraamountheorshepaidforsellingnumberof\\ pairsofshoes\times numberofpairofshoes\end{array}\right)\\ wherenumberofpairofshoessold=n\end{array}$

Thus, the expression for the total earned when he or she sold $n$ number of shoes is $\$150+\left(\$2\times n\right)$

Hence, the required expression is $\$150+\left(\$2\times n\right)$ .