Chapter A.9, Problem 112AYU

To determine

To find: The commission variation of the salesperson.

Answer to Problem 112AYU

The salesperson’s commission ranges from $\$105$ to $\$1225$.

Explanation of Solution

Given that a used car salesperson is paid a commission of $25 plus $40\%$ of the selling price in excess of owner’s cost.

$\text{i}\text{.e}., \text{the salesperson’s commission }=\hspace{0.17em}25\hspace{0.17em}+\hspace{0.17em}\frac{40}{100}\hspace{0.17em}\times \hspace{0.17em}\left(\text{selling price in excess of owner’s cost}\right)$

Also given that the selling price will be at least owner’s cost plus $\$200$ and at most owner’s cost plus $\$3000$.

Let $\times$ be the owner’s cost.

$\therefore x + 200 \le \text{selling price} \le x + 3, 000$

If the selling price is $x + 200$, then the excess amount is $\$25 + \left(0.40*200\right) = \$105.$

If the selling price is $x + 3, 000$, then the excess amount $\$25 + \left(0.40*3000\right) = \$1225$

∴ The salesperson’s commission ranges from $\$105$ to $\$1225$.