To solve this problem, we need to determine how many guests can be served with 12 pounds of chocolate if each guest eats [tex]\(\frac{3}{4}\)[/tex] pounds of chocolate. Here are the detailed steps:
1. Determine the total amount of chocolate available:
We are given that there are 12 pounds of chocolate available.
2. Determine the chocolate consumption per guest:
Each guest consumes [tex]\(\frac{3}{4}\)[/tex] pounds of chocolate.
3. Calculate the number of guests that can be served:
To find the number of guests that can be served, we divide the total amount of chocolate by the amount of chocolate each guest consumes. This can be represented by the formula:
[tex]\[
\text{Number of guests} = \frac{\text{Total chocolate}}{\text{Chocolate per guest}}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
\text{Number of guests} = \frac{12}{\frac{3}{4}}
\][/tex]
5. Simplify the division:
To divide by a fraction, you multiply by its reciprocal. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
\text{Number of guests} = 12 \times \frac{4}{3}
\][/tex]
6. Carry out the multiplication:
[tex]\[
12 \times \frac{4}{3} = 16
\][/tex]
So, 16 guests can be served with 12 pounds of chocolate.
Therefore, the number of guests that can be served is:
[tex]\[
\boxed{16}
\][/tex]
