Problem 66 - Elementary and Intermediate Algebra

Question

Ian's credit-card bill indicates that he owes \(\$ 470 .\) He sends a check to the creditcard company for \(\$ 45,\) charges another \(\$ 160\) in merchandise, and then pays off another \(\$ 500\) of his bill. What is Ian's new balance?

Step-by-Step Solution

Answer

Ian's new balance is \( 85 \) dollars.

Step 1: Initial Balance

Start by noting Ian's initial credit card balance. According to the problem, Ian owes \( 470 \) dollars.

Step 2: First Payment

Subtract the amount Ian pays in his first check from the initial balance. This check is for \( 45 \) dollars. Initial balance: \( 470 \) Payment: \( 45 \) New balance: \( 470 - 45 = 425 \) dollars.

Step 3: New Charges

Next, add the new charges Ian makes to the balance. He charges \( 160 \) dollars in merchandise. Previous balance: \( 425 \) New charges: \( 160 \) New balance: \( 425 + 160 = 585 \) dollars.

Step 4: Second Payment

Finally, subtract the second payment Ian makes from the new balance. He pays off another \( 500 \) dollars. Previous balance: \( 585 \) Additional Payment: \( 500 \) New balance: \( 585 - 500 = 85 \) dollars.

Key Concepts

Initial Balance

When dealing with credit card balances, the initial balance is the amount of money you owe before making any new transactions. It's essential to know this figure to accurately track how payments and charges affect your debt. In Ian's case, his initial balance is \(\$470\). This means before he makes any payments or new charges, he already owes this amount. Always start your calculations with the initial balance. This figure provides a baseline for understanding how your financial activities influence your total debt.

Payments

Payments refer to the money you send to reduce your credit card debt. Payments are subtracted from your current balance. For Ian, he starts by sending a payment of \(\$45\). After this payment, his new balance is reduced to \(\$425\) \[470 - 45 = 425\].
Ian makes another significant payment of \(\$500\) later. This payment further decreases his balance to \(\$85\) \[585 - 500 = 85\].
Pay close attention to how each payment affects your balance, helping you maintain financial control. Frequent and larger payments can quickly reduce your debt.

New Charges

New charges are any additional expenses you put on your credit card, which increase your balance. For Ian, he adds \(\$160\) in new charges after making his initial payment. This increases his balance from \(\$425\) to \(\$585\) \[425 + 160 = 585\].
Each time you make a purchase with your credit card, it increases the total amount you owe. Like in Ian's example, it's crucial to record every new charge. Being aware of new charges helps you keep track of how your spending habits affect your overall balance.

Final Balance

The final balance is the amount you owe after accounting for all payments and new charges. To find the final balance, start with your initial balance, subtract any payments, and then add new charges.
In the example of Ian’s account:

• Initial balance: \(\$470\)
• First payment: \(\$45\), new balance: \(\$425\)
• New charges: \(\$160\), new balance: \(\$585\)
• Second payment: \(\$500\), final balance: \(\$85\)

This step-by-step approach ensures you accurately calculate your debt. Monitoring your final balance can help you make informed financial decisions, avoiding additional debt.