Chapter A.9, Problem 111AYU

To determine

To find: The variation of agent’s commission and percentage of commission variation.

Answer to Problem 111AYU

Agent’s commission varies from $\$45, 000$ to $\$95, 000$ inclusive. The percentage of commission varies from $5\%$ to $8.6\%$ inclusive.

Explanation of Solution

Given that the commission is scheduled as $\$45, 000$ plus $25\%$ of the selling price in excess of $\$900, 000$. It can be expressed as,

$\text{Commission} = 45, 000 + \left(\frac{25}{100}\right) \times \left(\text{Excess of selling price}\right)$

Also given that the selling price ranges between $\$900, 000$ and $\$1, 100, 000$ inclusive. It can be expressed as,

$900, 000 \le \text{selling price} \le 1, 100, 000$

If the selling price is $\$900, 000$, then the excess of selling price is $0$.

If the selling price is $\$1, 100, 000$, then

$\text{the excess of selling price} = 1, 100.000 - 900, 00 = 200, 000.$

Hence the agent’s commission varies as follows:

$\begin{array}{l}45, 000 + \left(\frac{25}{100}\right) \times \left(0\right) \le \text{commission} \le 45, 000 + \left(\frac{25}{100}\right) \times \left(200, 000\right)\hfill \\ 45, 000 \le \text{commission} \le 45, 000 + 50, 000\hfill \\ 45, 000 \le \text{commission} \le 95, 000\hfill \end{array}$

For the selling price $\$900, 000$, the agent’s commission $\$45, 000$

For the selling price $\$1, 100, 000$, the agent’s commission $\$95, 000$