To determine how many cups of butter Joaquin will need, we start by considering the original recipe and the number of people it serves.
1. The original recipe serves 5 people and uses [tex]\(\frac{1}{2}\)[/tex] cup of butter.
2. Joaquin needs the recipe to serve 28 people.
First, we need to find the scaling factor, which tells us how many times the original recipe needs to be multiplied to serve the desired number of people:
[tex]\[
\text{Scaling factor} = \frac{\text{Required number of serves}}{\text{Original number of serves}} = \frac{28}{5}
\][/tex]
Calculating the scaling factor:
[tex]\[
\frac{28}{5} = 5.6
\][/tex]
With this scaling factor, we now determine how many cups of butter are needed for 28 people by multiplying the amount of butter in the original recipe by the scaling factor:
[tex]\[
\text{Butter needed} = \left(\frac{1}{2} \text{ cup}\right) \times 5.6
\][/tex]
Converting [tex]\(\frac{1}{2}\)[/tex] to a decimal gives us 0.5:
[tex]\[
\text{Butter needed} = 0.5 \times 5.6
\][/tex]
Performing the multiplication:
[tex]\[
0.5 \times 5.6 = 2.8
\][/tex]
Therefore, Joaquin will need 2.8 cups of butter to make his chocolate chip cookies for 28 people.
The correct answer from the given options is:
[tex]\[ 2 \frac{4}{5} \text{ cups} \][/tex]
which is the same as 2.8 cups.
