Answer :
Alright, let's break this down step by step.
1. Calculate the number of sandwiches needed:
Derek expects that for every 10 people, 11 sandwiches will be eaten. Since there are 300 people attending the picnic:
[tex]\[
\text{Number of sandwiches} = \left( \frac{300 \text{ people}}{10 \text{ people}} \right) \times 11 \text{ sandwiches}
\][/tex]
Simplifying this:
[tex]\[
\frac{300}{10} = 30, \quad 30 \times 11 = 330 \text{ sandwiches}
\][/tex]
So, the total number of sandwiches needed is 330 sandwiches.
2. Calculate the pounds of meat needed:
Derek knows that 20 pounds of meat will make 90 sandwiches. We need to determine how much meat is required for 330 sandwiches. We set up a proportion to find the solution:
[tex]\[
\frac{20 \text{ pounds}}{90 \text{ sandwiches}} = \frac{x \text{ pounds}}{330 \text{ sandwiches}}
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \left( \frac{20 \text{ pounds}}{90 \text{ sandwiches}} \right) \times 330 \text{ sandwiches}
\][/tex]
Simplifying this:
[tex]\[
x = \frac{20 \times 330}{90} = \frac{6600}{90} = 73.33333333333333 \text{ pounds}
\][/tex]
Therefore, Derek should purchase [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat to make 330 sandwiches for the 300 people attending the picnic. This matches with the given result.
1. Calculate the number of sandwiches needed:
Derek expects that for every 10 people, 11 sandwiches will be eaten. Since there are 300 people attending the picnic:
[tex]\[
\text{Number of sandwiches} = \left( \frac{300 \text{ people}}{10 \text{ people}} \right) \times 11 \text{ sandwiches}
\][/tex]
Simplifying this:
[tex]\[
\frac{300}{10} = 30, \quad 30 \times 11 = 330 \text{ sandwiches}
\][/tex]
So, the total number of sandwiches needed is 330 sandwiches.
2. Calculate the pounds of meat needed:
Derek knows that 20 pounds of meat will make 90 sandwiches. We need to determine how much meat is required for 330 sandwiches. We set up a proportion to find the solution:
[tex]\[
\frac{20 \text{ pounds}}{90 \text{ sandwiches}} = \frac{x \text{ pounds}}{330 \text{ sandwiches}}
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \left( \frac{20 \text{ pounds}}{90 \text{ sandwiches}} \right) \times 330 \text{ sandwiches}
\][/tex]
Simplifying this:
[tex]\[
x = \frac{20 \times 330}{90} = \frac{6600}{90} = 73.33333333333333 \text{ pounds}
\][/tex]
Therefore, Derek should purchase [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat to make 330 sandwiches for the 300 people attending the picnic. This matches with the given result.
