Problem 19 - Prealgebra

Question

Gasoline Tax New York state has one of the highest gasoline taxes in the country. If gas is currently selling at $$ 4.27\( for a gallon of regular gas and the tax rate is \)14.7 \%,$ how much of the price of a gallon of gas goes towards taxes?

Step-by-Step Solution

Answer

$0.63 of the price is for taxes.

Step 1: Understand the Problem

We are asked to find out how much of the price of a gallon of gasoline goes towards taxes in New York. The price of a gallon is $4.27 and the tax rate is 14.7%.

Step 2: Convert Percentage to Decimal

Transform the tax rate from a percentage to a decimal for calculation purposes. The tax rate is 14.7%, which converts to a decimal by dividing by 100.\[ 14.7\% = \frac{14.7}{100} = 0.147 \]

Step 3: Calculate the Tax Amount

Multiply the price of the gasoline by the decimal tax rate to determine the portion of the price that is due to tax:\[ \text{Tax} = 4.27 \times 0.147 \]

Step 4: Solve for the Tax Amount

Complete the calculation to find the tax amount:\[ \text{Tax} = 4.27 \times 0.147 = 0.62769 \]

Step 5: Round to Correct Units

Since prices are typically rounded to two decimal places, round 0.62769 to 0.63. So, $0.63 of the price of a gallon of gas goes toward taxes.

Key Concepts

Tax Calculation

Understanding how taxes are calculated can greatly help in many real-life situations—from understanding bills to making financial decisions. In our example, we are figuring out how much tax is added to the cost of a gallon of gasoline in New York. Here's a simple breakdown of how tax calculation works:

• Determine the original price of the item or service. In our case, it's $4.27 per gallon of gas.
• Find out the tax rate. For this exercise, the tax rate is 14.7%.
• Convert this percentage to a decimal to make calculations easier.
• Multiply the original price by the decimal tax rate. This product will give you the amount of tax in dollars that is added to the original price.

Once you perform the multiplication, you have your tax dollar amount. This amount is what is added to the original cost, reflecting how much you actually pay at the pump, including taxes.

Converting Percentages to Decimals

Transforming percentages into decimals is a straightforward but crucial mathematical skill. This conversion is essential when dealing with percentage calculations because it's much easier to work with decimals during multiplication and division. To convert a percentage into a decimal, you simply divide the percentage by 100. This works because a percentage is essentially a fraction out of 100. For example, to convert 14.7% to a decimal:

• Start with the percentage: 14.7%
• Divide by 100 to shift the decimal two places to the left: \[ 14.7\% = \frac{14.7}{100} = 0.147 \]

Once you perform this simple division, the result is the decimal form of the percentage. Using the decimal form in calculations facilitates easy computation with other numbers.

Rounding Decimals

Rounding decimals simplifies numbers, making them easier to read and use in everyday activities. It's often necessary when dealing with financial figures, like prices, where currency is usually rounded to two decimal points for cents. When you round a decimal, you look at the digit in the place that you're considering for rounding:

• If this digit is 5 or greater, you increase the previous digit by one.
• If this digit is less than 5, you leave the previous digit as is.

For example, our tax calculation gave us a result of 0.62769 dollars:

• Since prices are shown to two decimal points, look at the number in the third decimal place—7.
• Since 7 is greater than 5, round the second decimal place up from 2 to 3.

Therefore, 0.62769 rounds to 0.63. This final rounded value accurately represents the tax amount included in the gallon of gasoline price.