Question

Solve. Charlene has a current balance of \(-\$ 1243\) on her credit card. During the month, she makes the transactions shown below. What will her balance be at the end of the month? $$\begin{array}{l|l} \text { Charges } & \\ \hline \text { Truman's } & \$ 58 \\ \hline \text { Dave's Diner } & \$ 13 \\ \hline \text { Fuel 'n Go } & \$ 15 \\ \hline \text { Finance charge } & \$ 18 \\ \hline \text { Payment } & \$ 150 \\ \hline \end{array}$$

Short answer

Answer: -\$ 1289

Step-by-step solution

Add the charges and finance charge together

Add all the charges and the finance charge: \(58 + 13 + 15 + 18 = 104\)

Subtract Charlene's payment

Subtract the payment that Charlene made: \(104 - 150 = -46\)

Add the result to Charlene's initial balance

Now, add the result from Step 2 to Charlene's initial balance: \((-\$1243) + (-\$46) = \$(-1243 - 46) = -\$1289\)

Final answer

So, Charlene's balance at the end of the month will be \(-\$ 1289\).

Key concepts

Simple Addition and Subtraction

Simple addition and subtraction are the fundamental building blocks of mathematics that form the basis for more complex calculations. Let's start with addition, which is the process of combining two or more numbers to get a total. For example, if Charlene spends \( \$58 \) at Truman's and then \( \$13 \) at Dave's Diner, her total spending on these two transactions can be calculated using simple addition: \( 58 + 13 = 71 \). This tells us that, combined, she has spent \( \$71 \).

Subtraction, meanwhile, is the process of taking one number away from another. If Charlene makes a payment of \( \$150 \), we subtract that from her total charges to determine how much her balance has changed: \( 104 - 150 = -46 \). In this context, we're looking at the reduction in her debt, hence subtraction illustrates the decrease in her credit card balance after the payment is applied. Learning to operate with addition and subtraction fluently is essential for managing finances, among many other real-life applications.

Solving Real-life Math Problems

When it comes to applying mathematics to real-life situations, understanding how to approach problems systematically is crucial. Charlene's scenario with her credit card is a typical real-life math problem. She doesn't just have to keep track of her expenditures and payments, but also needs to calculate her ending balance, factoring in various charges and credits.

First, we identify what needs to be calculated – the end-of-month balance. Next, all charges are added together to get a total amount of expenditure. After this, we calculate the impact of the payment made towards the balance. And finally, the new balance is ascertained by adding the subtotals to the initial balance. This step-by-step approach not only simplifies complex situations but also ensures accuracy in everyday financial decisions, such as budgeting, monitoring accounts, or planning for expenses.

Understanding Negative Numbers

Negative numbers represent values less than zero and they are particularly essential when dealing with debts or below zero temperatures. In Charlene's case, her credit card balance is represented by a negative number, indicating that she owes money. When she makes a transaction, such as spending \( \$58 \) at Truman's, it adds to her debt, moving the balance further away from zero. Conversely, when she makes a payment, it reduces her debt, moving her closer to a positive balance or zero.

The action of adding a negative number is equivalent to subtraction since it increases the debt (or moves further from zero). For instance, adding the negative payment to her balance: \( (-\$1243) + (-\$46) = -\$1289 \), signifies that her debt has increased by \( \$46 \), taking her even further into the red. Understanding negative numbers is imperative for accurately representing and calculating debts, as well as grasping the concept of deficits in various contexts.