Question

A real estate agent agrees to sell an apartment complex according to the following commission​ schedule: ​$50000 plus 20​% of the selling price in excess of ​$900000. Assuming that the complex will sell at some price between ​$900000 and ​$1300000 ​inclusive, over what range does the​ agent's commission​ vary? How does the commission vary as a percent of selling​ price?

Answer 1

The real estate agent's commission will vary between $50,000 and $130,000, based on a fixed amount plus a variable percentage of the selling price. The commission as a percentage of the selling price will decrease as the selling price increases.

Step-by-step explanation:

The real estate agent's commission structure consists of a fixed component of $50,000, plus 20% of the amount by which the selling price exceeds $900,000. Thus, if the complex sells at the minimum price of $900,000, the commission will be just the fixed $50,000. If the complex sells at the maximum price of $1,300,000, the commission will be $50,000 plus 20% of ($1,300,000 - $900,000), which equals $50,000 plus 20% of $400,000, which is $80,000. So the commission will be $50,000 + $80,000 = $130,000 at the maximum selling price. Therefore, the range over which the agent's commission can vary is between $50,000 and $130,000.

The commission as a percent of the selling price will be the fixed $50,000 divided by the selling price plus 20% of the amount over $900,000. This percentage will decrease as the selling price increases since the $50,000 becomes a smaller proportion of the total selling price.