To determine the maximum number of children that could be in the building at one time, we need to follow these steps:
1. Identify the usable square footage for each room:
- Room 1: 500 sq. ft.
- Room 2: 450 sq. ft.
- Room 3: 350 sq. ft.
2. Determine the required space per child:
- Each child requires 35 sq. ft.
3. Calculate the maximum number of children each room can accommodate:
For Room 1:
[tex]\[
\text{Number of children} = \frac{\text{Room 1 square footage}}{\text{Square footage per child}} = \frac{500}{35} = 14 \text{ children} \quad \text{(using floor division)}
\][/tex]
For Room 2:
[tex]\[
\text{Number of children} = \frac{\text{Room 2 square footage}}{\text{Square footage per child}} = \frac{450}{35} = 12 \text{ children} \quad \text{(using floor division)}
\][/tex]
For Room 3:
[tex]\[
\text{Number of children} = \frac{\text{Room 3 square footage}}{\text{Square footage per child}} = \frac{350}{35} = 10 \text{ children} \quad \text{(using floor division)}
\][/tex]
4. Calculate the total number of children that the building can accommodate by adding the number of children each room can accommodate:
[tex]\[
\text{Total number of children} = \text{Number of children in Room 1} + \text{Number of children in Room 2} + \text{Number of children in Room 3}
\][/tex]
[tex]\[
\text{Total number of children} = 14 + 12 + 10 = 36 \text{ children}
\][/tex]
Therefore, the maximum number of children that could be in the building at one time is 36.
The correct answer is not listed among the given options (a, b, c, d). However, according to the calculation, the maximum is 36 children.
