Problem 68 - Elementary Algebra

Question

A home valued at \(\$ 50,000\) is assessed \(\$ 900\) in real estate taxes. At the same rate, hor much are the taxes on a home valued at \(\$ 60,0000\) ?

Step-by-Step Solution

Answer

The taxes on a home valued at $60,000 are $1,080.

Step 1: Determine the Tax Rate for the First Home

The home is valued at \( \\( 50,000 \) and is assessed \( \\) 900 \) in taxes. To find the tax rate, divide the tax amount by the home value: \[ \text{Tax Rate} = \frac{900}{50,000} = 0.018 \]. Thus, the tax rate is \( 1.8\% \).

Step 2: Apply the Tax Rate to the Second Home Value

Now, apply the \( 1.8\% \) tax rate to the second home's value of \( \\( 60,000 \) to find its tax amount: \[ \text{Tax on Second Home} = 0.018 \times 60,000 = 1,080 \]. The taxes on the second home are \( \\) 1,080 \).

Key Concepts

Tax Rate Calculation

When we're talking about the tax rate, we're trying to understand how much tax is charged on a particular value, usually assessed as a percentage. This exercise involves calculating a tax rate based on the value of homes.
To find a tax rate, follow these simple steps:

• Identify the value of the home. In the original exercise, the first home was valued at \(50,000.
• Find out how much tax is being charged. The tax assessed on the first home was \)900.
• Divide the tax amount by the home value like this: \( \frac{900}{50,000} \). This division gives us the tax rate as a decimal: 0.018.

The final step is converting this decimal into a percentage by multiplying by 100, resulting in a tax rate of 1.8%. Keeping these steps in mind will help you calculate tax rates for any given value.

Percentage Problems

Understanding percentages is crucial as they allow you to express how much one number is relative to another. In tax rate calculation, we use percentages to represent the portion of the home’s value that is paid as tax.
Here’s how to work with percentage problems:

• Convert the percentage into a decimal. For example, 1.8% becomes 0.018 by dividing by 100.
• To find a percentage of a number, multiply the number by the decimal form of the percentage. This was seen in our exercise by calculating the tax on the second home valued at \(60,000: \( 60,000 \times 0.018 \).
• Remember, multiplying gives you the amount that represents the percentage you're calculating. For the home's tax, it was \)1,080.

These problem-solving steps are helpful in a variety of real-world situations beyond real estate taxes.

Real Estate Tax Problems

Real estate tax problems often involve understanding how taxes are applied to property values. These taxes are crucial for funding local services like schools and public roads.
To solve real estate tax problems, like the ones in the exercise, follow these steps:

• First, determine the tax rate for the property in question. This is usually a percentage of the property's value.
• Apply this tax rate to the value of the property to calculate the tax amount. Ensure you're using the correct decimal form of the percentage to perform this step accurately.
• Real estate taxes can vary greatly depending on local policies, so knowing how to calculate them helps in managing budgets and understanding homeownership costs.

Mastering these concepts is essential for anyone planning to buy or sell property, or simply managing their own real estate investments.