Question
How much commission will the realtor earn for selling a $175,000 home If the realtor earned an $10,254.30 commission, what was the price of the home?
Answers
GPT-4o mini
To determine how much commission the realtor earns for selling a $175,000 home, we first need to find the commission rate.
Given that the realtor earned a $10,254.30 commission, we can express this as a percentage of the home price:
1. Let \( P \) be the price of the home in the second part of the question (which we will calculate).
2. Let \( R \) be the commission rate (as a decimal).
3. The formula for commission is:
\( \text{Commission} = R \times P \)
For the first part of your question, let's denote the commission rate for the $175,000 home as \( R \).
If we express the commission as a fraction of the sale price:
\[
R = \frac{\text{Commission}}{\text{Sale Price}} = \frac{\text{Commission}}{175,000}
\]
Assuming the amount of commission earned on the $175,000 home is the same as the $10,254.30 on the other home, we can set up the equation:
\[
10,254.30 = R \times 175,000
\]
To find \( R \):
\[
R = \frac{10,254.30}{175,000}
\]
Calculating \( R \):
\[
R \approx 0.0586 \text{ or } 5.86\%
\]
Now, if we want to find the price of the home given a $10,254.30 commission, we use the same commission rate \( R \):
\[
10,254.30 = R \times P
\]
Replacing \( R \):
\[
10,254.30 = 0.0586 \times P
\]
To find \( P \):
\[
P = \frac{10,254.30}{0.0586} \approx 175,000
\]
So, the price of the home where the realtor earned a $10,254.30 commission is approximately $175,000.
In conclusion, the realtor earns a commission of approximately **$10,254.30** on selling a **$175,000** home, assuming the same commission rate applies to both scenarios.
Given that the realtor earned a $10,254.30 commission, we can express this as a percentage of the home price:
1. Let \( P \) be the price of the home in the second part of the question (which we will calculate).
2. Let \( R \) be the commission rate (as a decimal).
3. The formula for commission is:
\( \text{Commission} = R \times P \)
For the first part of your question, let's denote the commission rate for the $175,000 home as \( R \).
If we express the commission as a fraction of the sale price:
\[
R = \frac{\text{Commission}}{\text{Sale Price}} = \frac{\text{Commission}}{175,000}
\]
Assuming the amount of commission earned on the $175,000 home is the same as the $10,254.30 on the other home, we can set up the equation:
\[
10,254.30 = R \times 175,000
\]
To find \( R \):
\[
R = \frac{10,254.30}{175,000}
\]
Calculating \( R \):
\[
R \approx 0.0586 \text{ or } 5.86\%
\]
Now, if we want to find the price of the home given a $10,254.30 commission, we use the same commission rate \( R \):
\[
10,254.30 = R \times P
\]
Replacing \( R \):
\[
10,254.30 = 0.0586 \times P
\]
To find \( P \):
\[
P = \frac{10,254.30}{0.0586} \approx 175,000
\]
So, the price of the home where the realtor earned a $10,254.30 commission is approximately $175,000.
In conclusion, the realtor earns a commission of approximately **$10,254.30** on selling a **$175,000** home, assuming the same commission rate applies to both scenarios.