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:
[tex]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[/tex]
We can compute the commission rate of the agency as follows:
[tex]C_{A}=4.5\% \times (\$ 311,000) = \$13,995[/tex]
The commission rate for the agent is 30% of the amount the real estate agency gets, so:
[tex]T_{B}=30\% \times (\$13,995) = \$4198.5[/tex]
Therefore, The total amount of money the agency gets is:
[tex]T_{A}=C_{A}-T_{B} \\ \\ \therefore T_{A}=\$13,995-\$4198.5=\$9796.5[/tex]
_____________________________________
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
