Let's walk through the steps explicitly to understand the solution.
Given:
- The total number of residents on the third floor is 39.
- The marginal distribution for third floor residents is 33.3%.
We need to find the two numbers used to make this distribution. First, we interpret that the marginal distribution means that 33.3% of the total building’s residents live on the third floor. Now, let's break it down step by step:
1. Identify the total residents on the third floor: The total number of residents on the third floor is given as 39.
2. Convert the marginal distribution percentage to a decimal: The given marginal distribution for third floor residents is 33.3%. To work with this percentage in calculations, convert it to a decimal:
[tex]\[
33.3\% = \frac{33.3}{100} = 0.333
\][/tex]
3. Calculate the total number of residents in the entire building: Given that 33.3% of the total residents live on the third floor, we can calculate the total number of residents (let's call this [tex]\( T \)[/tex]):
[tex]\[
\text{Total residents in the building} = \frac{\text{Third floor residents}}{\text{Marginal distribution third floor}}
\][/tex]
Substituting the known values:
[tex]\[
T = \frac{39}{0.333}
\][/tex]
4. Perform the division:
[tex]\[
T = \frac{39}{0.333} = 117
\][/tex]
So, the total number of residents in the entire building is 117.
5. Verify the number of third floor residents from this total: To ensure the calculation is correct, we need to verify this number. We know that 33.3% of the total residents live on the third floor:
[tex]\[
\text{Third floor residents} = 0.333 \times 117
\][/tex]
Performing the multiplication:
[tex]\[
0.333 \times 117 = 39
\][/tex]
Thus, the two numbers used to make the marginal distribution are [tex]\( 39 \)[/tex] (the number of residents on the third floor) and [tex]\( 117 \)[/tex] (the total number of residents in the entire building).
