To determine the total amount of appetizers [tex]\( A \)[/tex] Mike needs to prepare in terms of [tex]\( p \)[/tex], the number of people attending the party, follow these steps:
1. Calculate the initial number of appetizers:
Mike starts with 4 trays, each containing 5 appetizers. Therefore, the total initial number of appetizers is:
[tex]\[
4 \times 5 = 20
\][/tex]
2. Calculate the additional appetizers needed for the guests:
Mike wants to prepare 2 appetizers for each person attending the party. Therefore, for [tex]\( p \)[/tex] people, the total number of additional appetizers needed is:
[tex]\[
2 \times p = 2p
\][/tex]
3. Combine the initial appetizers with the additional appetizers:
The total number of appetizers [tex]\( A \)[/tex] will be the initial number plus the number of additional appetizers:
[tex]\[
A = 20 + 2p
\][/tex]
So, the correct representation for [tex]\( A \)[/tex], the total amount of appetizers Mike needs to make, in terms of [tex]\( p \)[/tex], the number of people attending the party, is:
[tex]\[
\boxed{A = 20 + 2p}
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{B. \, A = 20 + 2p}
\][/tex]
