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Mike is catering a party. He plans on having 4 trays of 5 appetizers each on the buffet at the beginning of the party and will rotate in new trays as those become empty. To ensure that he does not run out of appetizers, he will make 2 appetizers per person in addition to the initial number put out on the buffet.

Which of the following represents [tex]\(A\)[/tex], the amount of appetizers Mike needs to make, in terms of [tex]\(p\)[/tex], the number of people attending the party?

A. [tex]\(A = 2 - 20p\)[/tex]
B. [tex]\(A = 20 + 2p\)[/tex]
C. [tex]\(A = 20p + 2\)[/tex]
D. [tex]\(A = 2p - 20\)[/tex]



Answer :

GinnyAnswer
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]

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