Problem 41 - Algebra 1

Question

Writing You decide to buy two rings from an outdoor vendor. One ring costs $$ 10.89 .\( The other ring costs $$ 12.48 . The sales tax is \)8 \% .\( The vendor uses a calculator to obtain the price including sales tax for both rings and gets $$ 24.37 .\) What mistake did the vendor make?

Step-by-Step Solution

Answer

The mistake the vendor made was undercharging the customer. The correct total price of the rings should be $25.24, not $24.37. So, the vendor undercharged the customer by $0.87.

Step 1: Calculating total price of the rings

Add the prices of both the rings: \(10.89 + 12.48 = 23.37\) dollars. This is the total cost of the rings before tax.

Step 2: Calculating the correct sales tax

Multiply the total price by the sales tax rate to calculate the tax: \(23.37 * 0.08 = 1.87\) dollars. This is the correct sales tax that should be added to the total ring cost.

Step 3: Calculating the correct total price after tax

Add the sales tax to the total cost of the rings before tax: \(23.37 + 1.87 = 25.24\) dollars This is the correct total price of the rings including the sales tax.

Step 4: Identifying the mistake

The vendor gave the total amount as $24.37 which is less than the correctly calculated total amount of \$25.24, so the mistake the vendor made was undercharging the customer.

Step 5: Correcting Vendor's calculation mistake

The correct total price of the rings including the sales tax should be $25.24, not $24.37. The vendor undercharged the customer by $0.87.

Key Concepts

Price Calculation

When determining the cost of items before tax, it's crucial to sum up their individual prices accurately. In this scenario, you have two rings; one costs $10.89 and the other $12.48. To find the total cost before tax, add these prices together:

• First Ring: $10.89
• Second Ring: $12.48
• Total Before Tax = $10.89 + $12.48 = $23.37

This calculation gives you the total amount you are initially spending on the rings. Always make sure your figures are correct to avoid errors that could impact further calculations.

Addition of Prices

Adding prices may seem straightforward, but it's easy to make errors if you're not careful. In the exercise, the vendor had to combine the prices of two rings. Simple mistakes can occur in this step, such as mistaking a digit or misplacing a decimal point.

• Verify that all values are aligned correctly by decimal points.
• Double-check each digit’s addition to avoid simple errors.

These steps are critical because they affect the total before tax. A small mistake here can lead to larger issues in subsequent calculations.

Percentage Calculation

Calculating a percentage for sales tax involves converting the percentage into a decimal and multiplying by the total price before tax. The sales tax rate in this case is 8%. To find the tax amount:

• Convert the percentage to decimal: 8% = 0.08
• Multiply by the total before-tax cost: $23.37 x 0.08 = $1.87

This gives you the amount of sales tax that needs to be added to the price of the items. Understanding percentage calculations is crucial for accurately determining final costs.

Error Analysis

Analyzing errors helps pinpoint issues in calculations and ensures accurate pricing. The vendor made a mistake by giving the total as $24.37 instead of the correct $25.24. Here's how you can identify and analyze this error:

• Recalculate the total cost using step-by-step methods to ensure accuracy.
• Compare your calculated total to the vendor's reported amount.
• The difference between $25.24 and $24.37 is $0.87, indicating undercharging.

Understanding where the error happened allows you to make the necessary corrections and ensures you pay or charge the correct amount. It's crucial for transparency and correctness in financial transactions.