Question

At a real estate​ agency, an agent sold a house for ​$311,000. The commission rate is 4.5​% for the real estate agency and the commission rate for the agent is 30​% of the amount the real estate agency gets. How much did the agency make on the​ house? How much did the agent earn in​ commission

Answer 1

In this problem, we know that:

• An agent sold a house for ​$311,000 at a real estate​ agency.
• The commission rate is 4.5​% for the real estate agency.
• The commission rate for the agent is 30​% of the amount the real estate agency gets.

So the questions are two.

Let's name:

`T_(A): The \ total \ amount \ of \ money \ the \ agency \ gets \\ \\ C_(A): The \ commission \ rate \ for \ the \ agency \\ \\ T_(B):The \ amount \ of \ money \ the \ agent \ earns \ in \ commission`

We can compute the commission rate of the agency as follows:

`C_(A)=4.5\% * (\$ 311,000) = \$13,995`

The commission rate for the agent is 30​% of the amount the real estate agency gets, so:

`T_(B)=30\% * (\$13,995) = \$4198.5`

Therefore, The total amount of money the agency gets is:

`T_(A)=C_(A)-T_(B) \\ \\ \therefore T_(A)=\$13,995-\$4198.5=\$9796.5`

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Finally, to sum up:

Q1. How much did the agency make on the​ house?

The agency makes $9796.5

Q2. How much did the agent earn in​ commission?

The agent earns in commission $4198.5