Problem 135 - Beginning and Intermediate Algebra

Question

Solve each problem. Linda owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00\). She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?

Step-by-Step Solution

Answer

Linda still owes \$ 323.83.

Step 1 - Calculate the total amount credited

Linda returns two items and receives credits for them. Add the amounts of the returned items: \( \$ 35.90 + \$ 150.00 = \$ 185.90 \)

Step 2 - Calculate the new balance after credits

Subtract the total credited amount from the initial amount owed: \( \$ 870.00 - \$ 185.90 = \$ 684.10 \)

Step 3 - Add the new purchases to the balance

Linda makes three new purchases. Add these amounts to the balance: \( \$ 684.10 + \$ 82.50 + \$ 10.00 + \$ 10.00 = \$ 786.60 \)

Step 4 - Subtract the payment made

Linda makes a payment of \$ 500. Subtract this from the balance: \( \$ 786.60 - \$ 500.00 = \$ 286.60 \)

Step 5 - Add the finance charge

Lastly, add the finance charge to the new balance: \( \$ 286.60 + \$ 37.23 = \$ 323.83 \)

Key Concepts

Financial Calculations

Understanding financial calculations is essential for solving many real-world problems. In this exercise, we're dealing with a MasterCard account balance, which requires us to track multiple transactions. This is a common financial situation that many people face.

When managing your finances, it's important to:

• Keep track of all credits and debits
• Ensure that all transactions are accounted for
• Be aware of any finance charges or fees

In this example, Linda needs to calculate her remaining balance by considering all returns, purchases, payments, and finance charges. Each of these steps involves basic arithmetic operations, but they need to be performed in the correct order to ensure an accurate result.

Addition and Subtraction

At the core of this exercise are the addition and subtraction operations.

Let's break them down step-by-step:

• Addition: Adding the amounts of returned items to find the total credit. Then, adding new purchases to the existing balance.
• Subtraction: Subtracting the total credit from the initial debt. Then, subtracting the payment made from the current balance to find the new owed amount.

Each step requires careful arithmetic operations:

• Returned items: Add \(\text{\$35.90 + \$150.00 = \$185.90}\). This is the total credit Linda receives.
• Crediting returns: Subtract credits from the original debt: \(\text{\$870.00 - \$185.90 = \$684.10}\).
• New purchases: Add purchases: \(\text{\$684.10 + \$82.50 + \$10.00 + \$10.00 = \$786.60}\).
• Payment: Subtract payment from current balance: \(\text{\$786.60 - \$500.00 = \$286.60}\).
• Finance charge: Add finance charge to new balance: \(\text{\$286.60 + \$37.23 = \$323.83}\).

Notice how each transaction moves you step-by-step towards calculating the final amount owed.

Real-World Math Problems

Applying math to real-world problems makes it easier to see its value.

Understanding financial transactions through this exercise shows you how math works in everyday life. Keeping track of a credit card balance, for instance, involves several steps:

• Returning items for credit: affects your balance positively by reducing what you owe.
• Making purchases: increases the amount you owe.
• Making payments: reduces your debt.
• Dealing with finance charges: slightly increases what you owe due to interest or fees.

Each of these activities requires simple arithmetic, but when combined, they provide a clear picture of how a financial balance can change over time. This example helps underscore the necessity of basic math skills in managing personal finances efficiently.

Step-by-Step Solution

Following a step-by-step solution is crucial for solving complex problems accurately.

Here's a breakdown of the process in Linda's exercise:

1. Calculate the total amount credited:
   Combine the returned items: \(\text{\$35.90 + \$150.00 = \$185.90}\).
2. Subtract the total credit from the initial debt:
   Reduce her initial owed amount by the credits: \(\text{\$870.00 - \$185.90 = \$684.10}\).
3. Add the amount of new purchases:
   Increase the balance with new purchases: \(\text{\$684.10 + \$82.50 + \$10.00 + \$10.00 = \$786.60}\).
4. Subtract the payment made:
   Deduct the payment from the current balance: \(\text{\$786.60 - \$500.00 = \$286.60}\).
5. Add the finance charge:
   Include the finance charge to find the final owed amount: \(\text{\$286.60 + \$37.23 = \$323.83}\).

This method breaks down the problem into manageable parts, making it easier to follow and ensuring no steps are missed. Each operation builds upon the previous, leading logically to the final solution.