Problem 57 - Algebra 1: Concepts and Skills

Question

Turner Field in Atlanta, Georgia, has 49, 831 seats. Jacobs Field in Cleveland, Ohio, has \(43,368\) seats. How many seats need to be added to Jacobs Field for it to have as many seats as Turner Field?

Step-by-Step Solution

Answer

6,463 seats need to be added to Jacobs Field for it to have as many seats as Turner Field.

Step 1: Identify the number of Seats at each Stadium

From the exercise, we know that Turner Field has \(49,831\) seats and Jacobs Field has \(43,368\) seats.

Step 2: Subtract the number of seats at Jacobs Field from Turner Field

Subtract \(43,368\) from \(49,831\) to find out how many seats Jacobs Field is short of compared to Turner Field.

Step 3: Perform the Calculations

Doing the subtraction, \(49,831 - 43,368 = 6,463\) we find that 6,463 seats are needed.

Key Concepts

Algebraic Problem Solving

Algebraic problem solving involves finding unknown values by applying mathematical operations within the framework of algebra. In the context of our exercise, we're not explicitly dealing with an algebraic expression, yet the process of resolving the problem benefits from an algebraic mindset. First, understand the problem, identify what you know and what you need to find out. Here, we know the numbers of seats in both Turner Field and Jacobs Field, and we need to find the difference.

In a more complex algebraic problem, we might let 'x' represent the unknown number of seats needed. We'd then set up an equation to solve for 'x'. However, with simple subtraction at hand, we often bypass the formalities of algebra and solve it directly. This doesn't mean that the systematic approach of algebra isn't there; it's just simplified for an elementary task. It's important to recognize that even when not visible, algebraic thinking is a powerful tool in solving mathematical word problems.

Subtracting Large Numbers

Subtracting large numbers, crucial for solving our exercise, seems daunting but becomes simple with the right technique. Here’s a tip: always align the numbers by their place value columns. So for our example, you would write the numbers vertically:

• 49,831
• - 43,368

Subtract each column starting from the right, borrowing from the next column if necessary. Should you end up with a negative number, carry over from the left. When set up properly, subtraction of large numbers becomes as straightforward as subtracting single digits.

Emphasize the importance of proper alignment, borrowing, and carrying over when teaching subtraction as these are foundational skills that will be essential in more complex arithmetic, including algebra.

Mathematical Word Problems

Mathematical word problems, like the example provided, merge reading comprehension with mathematical reasoning. There are a few steps we can follow to make solving these problems easier:

• Read the problem carefully to understand what it is asking.
• Identify the data given and what you need to find.
• Visualize the problem if possible, and organize the information logically.
• Choose the appropriate operation to use based on the context (in this case, subtraction).
• Solve the problem and check your work to ensure it makes sense within the context of the question.

For our seating problem, we read about Turner Field and Jacobs Field, identified their seat counts, visualized the scenario, used subtraction to find the difference, and arrived at the solution. Word problems are a great way to apply math in real-world contexts, reinforcing how valuable mathematical skills are in everyday life.