To determine the number of model [tex]\( B \)[/tex] cars the factory should make next year, we need to follow a few steps to calculate the proportion of people who prefer model [tex]\( B \)[/tex] and then apply that proportion to the total number of cars the factory plans to produce.
1. Total number of people surveyed:
The total number of people surveyed is 80.
2. Number of people who prefer model [tex]\( B \)[/tex]:
From the table, 15 people indicated they would prefer model [tex]\( B \)[/tex].
3. Calculate the proportion of people who prefer model [tex]\( B \)[/tex]:
[tex]\[
\text{Proportion of people who prefer model } B = \frac{\text{Number of people who prefer model } B}{\text{Total number of people surveyed}} = \frac{15}{80}
\][/tex]
Simplifying the fraction, we get:
[tex]\[
\text{Proportion of people who prefer model } B = 0.1875
\][/tex]
4. Total number of cars to be made:
The factory plans to produce 40,000 cars next year.
5. Calculate the number of model [tex]\( B \)[/tex] cars to make:
Using the proportion calculated, we can find the number of model [tex]\( B \)[/tex] cars by multiplying the total number of cars by the proportion of people who prefer model [tex]\( B \)[/tex]:
[tex]\[
\text{Number of model } B \text{ cars to make} = \text{Proportion of people who prefer model } B \times \text{Total number of cars}
\][/tex]
[tex]\[
\text{Number of model } B \text{ cars to make} = 0.1875 \times 40000 = 7500
\][/tex]
Therefore, the factory should make 7,500 model [tex]\( B \)[/tex] cars next year.
