Problem 136 - Beginning and Intermediate Algebra

Question

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Step-by-Step Solution

Answer

Marcial still owes \$712.39\.

Step 1: Calculate total credits for returned items

Add the amounts for the returned items: a) \$36.89 \b) \$29.40 \c) \$113.55 \[ 36.89 + 29.40 + 113.55 = 179.84 \]Marcial receives a total credit of \$179.84\ on his account.

Step 2: Determine new balance after credits

Subtract the total credit from the initial amount owed: \[ 679.00 - 179.84 = 499.16 \]The new balance after the credits is \$499.16\.

Step 3: Calculate total for all new purchases

Add the amounts of all new purchases:a) \$135.78 \b) \$412.88 \c) \$20.00 \d) \$20.00 \[ 135.78 + 412.88 + 20.00 + 20.00 = 588.66 \]Marcial makes total new purchases of \$588.66\.

Step 4: Determine new balance after adding purchases

Add the total purchases to the balance after credits: \[ 499.16 + 588.66 = 1087.82 \]The new balance after the purchases is \$1087.82\.

Step 5: Calculate new balance after the payment

Subtract Marcial's payment from the new balance: \[ 1087.82 - 400.00 = 687.82 \]The new balance after the payment is \$687.82\.

Step 6: Add the finance charge

Add the finance charge to the new balance: \[ 687.82 + 24.57 = 712.39 \]After adding the finance charge of \$24.57\, the total amount Marcial still owes is \$712.39\.

Key Concepts

Addition and Subtraction of Decimals

Understanding how to add and subtract decimals is crucial for solving real-world problems that involve money, measurements, and other quantifiable factors. When dealing with decimals, ensure you align the numbers by the decimal point before performing the addition or subtraction. This way, each decimal place is properly accounted for, ensuring accurate results. For instance, when Marcial receives credit for returned items and needs to subtract these amounts from what he owes, you line up: \(36.89 + 29.40 + 113.55\) which totals \(179.84\). After adding them up correctly, subtracting \(179.84\) from \(679.00\) gives \(499.16\). These steps show how essential precision in decimal operations is to maintain accurate finance records.

Order of Operations

The order of operations is a set of rules that helps you determine the sequence in which multiple operations need to be carried out. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) can help you remember these rules. In Marcial's case, after receiving credits, he made new purchases, resulting in added amounts: \(135.78 + 412.88 + 20.00 + 20.00 = 588.66\). However, you must first calculate the credit before changes like purchases and payments. Correct sequencing using the order of operations ensures financial calculations are accurate and reliable. This helps in managing personal finances more effectively and avoiding costly errors.

Credit and Finance Calculations

Credit and finance calculations are critical life skills, particularly when managing personal debt and understanding charges. For Marcial's scenario, it involved tracking credits, new purchases, payments, and finance charges. Initially, he owed \(\text{\textdollar}679.00\), received \(\text{\textdollar}179.84\) in credits which reduced the balance to \(\text{\textdollar}499.16\). Adding \(\text{\textdollar}588.66\) for new purchases increased this to \(\text{\textdollar}1087.82\). A payment of \(\text{\textdollar}400\) reduced it to \(\text{\textdollar}687.82\), and a finance charge of \(\text{\textdollar}24.57\) brought the total owed to \(\text{\textdollar}712.39\). By keeping track of all these figures accurately, one can ensure that all credits and debits are accounted for and debts are managed properly.