Problem 29 - Algebra A Combined Function

Question

Solve the following. A human factors expert recommends that there be at least 9 square feet of floor space in a college classroom for every student in the class. Find the minimum floor space that 40 students need.

Step-by-Step Solution

Answer

The minimum floor space needed is 360 square feet.

Step 1: Understand the Problem

The problem requires us to determine the minimum floor space needed for a classroom that must accommodate 40 students, with each student needing at least 9 square feet.

Step 2: Identify Key Information

We know that each student requires 9 square feet and there are 40 students. Therefore, to find the total floor space, we multiply the number of students by the space available per student.

Step 3: Set Up the Equation

The equation for calculating the total floor space is given by multiplying the number of students (40) by the square footage per student (9). The equation is:\[\text{Total Floor Space} = 40 \times 9\]

Step 4: Calculate the Total Floor Space

By performing the multiplication, we find the total floor space needed:\[\text{Total Floor Space} = 40 \times 9 = 360 \text{ square feet}\]

Step 5: Verify the Solution

The calculation shows that 360 square feet is needed for 40 students when each requires 9 square feet. This is consistent with the problem's requirements.

Key Concepts

Equation Setup

In this problem, our main task is to find out the minimum total floor space required for 40 students in a classroom, with each needing 9 square feet.
Understanding how to set up the equation is crucial for solving problems like these, where you need to combine two or more quantities.

To start with the equation setup:

• Identify what you're solving for – here, it’s the total floor space.
• Determine the quantities involved – in this case, the number of students, 40, and the area needed by each student, 9 square feet.

An equation is formed by relating these quantities.
The formula becomes:
\[\text{Total Floor Space} = \text{Number of Students} \times \text{Space per Student}\]
This equation will help provide the solution by organizing the information clearly.

Multiplication

Once the equation \[\text{Total Floor Space} = 40 \times 9\] is set up, multiplication is the core operation to carry out.
Multiplying 40 students by 9 square feet per student calculates the total space needed.

Let's simplify this step by breaking down the multiplication:

• First, multiply 40 by 9.
• This equals 360.

The multiplication step tells us that the total floor space required is 360 square feet.
Each step involves simple arithmetic, which confirms the process is correct.

Verification of Solution

Verification is the final step ensuring that the calculated solution fulfills the problem’s requirements.
It's crucial to verify the total calculated floor space matches the conditions given in the problem.

To verify:

• Check that the equation solved meets the minimum floor space per student.
• Confirm there are or more adequate total square feet available for 40 students.

Since we calculated 360 square feet, and the requirement is for each student to have 9 square feet, our solution is verified.
Each student adequately fits within the calculated space, meeting the specified conditions of the original problem statement, ensuring accurate and complete problem-solving.