Problem 53 - Algebra 1: Concepts and Skills

Question

At a concert you buy a hat for \(10.00, a hot dog for \)2.75, and nachos for $3.50. There is a 6% sales tax on the hat. Your calculator follows the established order of operations. Write a keystroke sequence for the amount you owe. Then find the amount you owe. HINT: 6% 0.06

Step-by-Step Solution

Answer

The total amount owed is $16.85.

Step 1: Calculate the total price of the food

Firstly, add up the prices of the hat, hot dog, and nachos. This can be done as follows: \(10.00 + 2.75 + 3.50 = 16.25\)

Step 2: Calculate the sales tax

Next, calculate the sales tax on the hat. It will be calculated as follows: \(10.00 \times 0.06 = 0.60\)

Step 3: Calculate the total amount owed

Lastly, add the sales tax to the total price calculated in the first step. This can be done as follows: \(16.25 + 0.60 = 16.85\)

Key Concepts

sales tax calculation

Sales tax is a percentage of the price of a product that is added to the total cost at the time of purchase. It varies from place to place and is applied to specific items. In this scenario, sales tax only applies to the hat. The hat costs \(10.00, and the sales tax rate is 6%, or 0.06 in decimal form.

To calculate the sales tax due for the hat, multiply its cost by the sales tax rate:

• Multiply the hat’s price: \(10.00 \times 0.06 = 0.60\)

This means that the sales tax for the hat will be \)0.60. This amount needs to be added to your total purchase amount to get the final amount owed.

total price calculation

Total price calculation involves adding up the cost of all items purchased and any additional costs such as sales tax. In this task, you are dealing with a hat, a hot dog, and nachos. Firstly, sum up the initial costs:

• Add the prices of the hat, hot dog, and nachos: \(10.00 + 2.75 + 3.50 = 16.25\)

This total represents the combined cost of the three items without the sales tax. Afterward, you include the sales tax calculated for applicable items, which in this case is only applicable to the hat:

• Add the sales tax: \(16.25 + 0.60 = 16.85\)

Thus, the total price you will ultimately owe is $16.85. Understanding this process helps ensure you are ready for any purchases involving multiple items and taxes.

keystroke sequence

A keystroke sequence refers to the order in which you should enter numbers and operations into a calculator to solve a problem using the correct order of operations. This ensures that you arrive at the correct final total. The order of operations typically follows "PEMDAS" (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

For this particular calculation, follow these steps with your calculator:

• Enter the total item cost without tax: 10.00 + 2.75 + 3.50
• Press the equals button to get 16.25
• Calculate sales tax: 10.00 \(\times\) 0.06
• Press the equals button to get 0.60
• Add the sales tax to the item total: 16.25 + 0.60
• Press equals to find the final amount: 16.85

This sequence ensures that each operation is completed in the correct order, so you accurately calculate the amount you owe for your purchases. Properly using keystrokes can save you from manual errors in everyday transactions.