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For each home in Dutch County, the amount of property tax is $p$ perce
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04 Aug 2025, 14:05
04 Aug 2025, 14:05
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Question Stats:
92% (00:52) correct
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For each home in Dutch County, the amount of property tax is $p$ percent of the value of the home. The property tax on a home whose value is \($ 55,000\) is \($ 5,500\).
Quantity A |
Quantity B |
The property tax on a home in Dutch County whose value is \($65,000\) |
\($ 6,600\) |
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Re: For each home in Dutch County, the amount of property tax is $p$ perce
[#permalink]
14 Aug 2025, 22:43
14 Aug 2025, 22:43
Expert Reply
Given:
- Property tax is $p %$ of the home value.
- For a $\(\$ 55,000\)$ home, property tax $\(=\$ 5,500\)$.
Step 1: Find the tax rate $p$
Property tax $=p % \times$ home value
Given:
$$
\(5500=\frac{p}{100} \times 55000\)
$$
Solve for $p$ :
$$
\(\begin{gathered}
5500=55000 \times \frac{p}{100} \\
\frac{5500}{55000}=\frac{p}{100} \\
0.1=\frac{p}{100} \\
p=10
\end{gathered}\)
$$
So, the property tax rate is $10 %$.
Step 2: Calculate property tax on a $\(\$ 65,000\)$ home
\(Tax=10\) % \(\times 65000=\frac{10}{100} \times 65000=6500\)
Compare Quantity A and Quantity B:
- Quantity $\(A=\$ 6,500\)$
- Quantity \(B = \$6,600\)
Answer:
- Quantity $\(B(\$ 6,600)\)$ is greater than Quantity $\(A(\$ 6,500)\)$.
Final conclusion:
Quantity B is greater.
- Property tax is $p %$ of the home value.
- For a $\(\$ 55,000\)$ home, property tax $\(=\$ 5,500\)$.
Step 1: Find the tax rate $p$
Property tax $=p % \times$ home value
Given:
$$
\(5500=\frac{p}{100} \times 55000\)
$$
Solve for $p$ :
$$
\(\begin{gathered}
5500=55000 \times \frac{p}{100} \\
\frac{5500}{55000}=\frac{p}{100} \\
0.1=\frac{p}{100} \\
p=10
\end{gathered}\)
$$
So, the property tax rate is $10 %$.
Step 2: Calculate property tax on a $\(\$ 65,000\)$ home
\(Tax=10\) % \(\times 65000=\frac{10}{100} \times 65000=6500\)
Compare Quantity A and Quantity B:
- Quantity $\(A=\$ 6,500\)$
- Quantity \(B = \$6,600\)
Answer:
- Quantity $\(B(\$ 6,600)\)$ is greater than Quantity $\(A(\$ 6,500)\)$.
Final conclusion:
Quantity B is greater.
gmatclubot
Re: For each home in Dutch County, the amount of property tax is $p$ perce [#permalink]
14 Aug 2025, 22:43
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