Derek is purchasing lunch meat for the class picnic. There are 300 people attending the picnic. Derek expects that for every 10 people, 11 sandwiches will be eaten, and that 20 pounds of meat will make 90 sandwiches. How much lunch meat should Derek buy?

A. [tex]$67 \frac{2}{3}$[/tex] pounds
B. 330 sandwiches
C. [tex]$73 \frac{1}{3}$[/tex] pounds
D. 110 pounds

To solve the problem of how much lunch meat Derek should buy for the class picnic, follow these steps:

1. Understand the problem requirements:
- There are 300 people attending the picnic.
- For every 10 people, 11 sandwiches will be consumed.
- 20 pounds of meat are needed to make 90 sandwiches.

2. Calculate the total number of sandwiches needed:
- First, figure out how many groups of 10 people there are in 300 people. Divide 300 by 10:
[tex]\[
\frac{300}{10} = 30
\][/tex]
- Each group of 10 people will eat 11 sandwiches, so for 30 groups:
[tex]\[
30 \times 11 = 330 \text{ sandwiches}
\][/tex]

3. Determine how much meat is needed for 330 sandwiches:
- Use the information that 20 pounds of meat makes 90 sandwiches. To find out how many pounds are needed for 330 sandwiches, set up a proportion:
[tex]\[
\frac{20 \text{ pounds}}{90 \text{ sandwiches}} = \frac{x \text{ pounds}}{330 \text{ sandwiches}}
\][/tex]
- Solve the proportion by cross-multiplying:
[tex]\[
20 \times 330 = 90 \times x
\][/tex]
[tex]\[
6600 = 90x
\][/tex]
[tex]\[
x = \frac{6600}{90} = 73.\overline{3} \text{ pounds}
\][/tex]

So, Derek should purchase approximately [tex]$73 \frac{1}{3}$[/tex] pounds of lunch meat for the picnic.