Problem 611 - Prealgebra

Question

Last month, Stan's take-home pay was \(\$ 3,816\) and his expenses were \(\$ 3,472\) . How much of his take-home pay did Stan have left after he paid his expenses?

Step-by-Step Solution

Answer

\( \$344 \)

Step 1: Understand the problem

Determine how much money Stan had left after his expenses by subtracting his total expenses from his take-home pay.

Step 2: Identify the given values

Stan's take-home pay is \( \$3,816 \) and his expenses are \( \$3,472 \).

Step 3: Set up the subtraction

Write the subtraction equation: \[ 3816 - 3472 \].

Step 4: Perform the subtraction

Calculate the result: \[ 3816 - 3472 = 344 \].

Step 5: State the result

After paying his expenses, Stan has \( \$344 \) left of his take-home pay.

Key Concepts

Arithmetic Operations

Arithmetic operations are the foundation of basic math. These operations include addition, subtraction, multiplication, and division. In this particular problem, we focus on subtraction. Subtraction helps us determine the difference between two numbers. It's the process of taking one number away from another. This method is used daily, whether balancing a budget or making change during a purchase. Understanding subtraction is vital for more complex math concepts.

To subtract correctly:

• Line up the numbers by their rightmost digits.
• Subtract each digit starting from the right and moving left.
• If the top digit is smaller than the bottom digit, borrow from the next left digit.

Subtraction Problems

Handling subtraction problems involves straightforward steps, but practice is essential. In our example with Stan's take-home pay, we used subtraction to find out how much was left after expenses.

Here’s a quick breakdown of the steps:

• Identify the numbers involved. Stan's income was \( \$3816 \) and his expenses \( \$3472 \).
• Set up the subtraction problem: \[ 3816 - 3472 = 344 \]
• Perform the subtraction starting from the rightmost digits. If ever we need to borrow, we simply reduce the next digit to the left by one and increase the current column by ten.

After the calculations, Stan's remaining money is \( \$344 \). This simple problem is a great example of how subtraction helps answer practical questions.

Problem Solving

Effective problem solving in math requires a systematic approach. Let's walk through the process using our current problem as a reference.

First, understand what’s being asked. The question is, 'How much money did Stan have left after paying his expenses?' This means we need to find the difference between his total income and his total expenses.

Next, identify the relevant information. Here, we know Stan's income and his expenses. With these numbers, we can set up a subtraction problem to find the solution.

Finally, perform the arithmetic operation required and interpret the result. By subtracting Stan's expenses from his income, we determine the remaining amount. This methodical approach can be applied to various math problems:

• Read the problem carefully.
• Identify and organize the necessary information.
• Set up the math operation (addition, subtraction, etc.)
• Perform the operation accurately.
• Review the solution for accuracy and completeness.

Using this structured problem-solving strategy ensures you handle math problems efficiently and effectively.