Answer :
To determine how much lunch meat Derek should buy for the picnic, let's break down the problem into a step-by-step solution.
1. Determine the number of sandwiches needed:
- Derek expects that for every 10 people, 11 sandwiches will be consumed.
- There are 300 people attending the picnic.
- To find out how many sandwiches are needed, calculate:
[tex]\[
\text{Number of sandwiches} = \left(\frac{\text{number of people}}{10}\right) \times \text{sandwiches per 10 people}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Number of sandwiches} = \left(\frac{300}{10}\right) \times 11 = 30 \times 11 = 330 \text{ sandwiches}
\][/tex]
2. Determine the amount of lunch meat needed:
- We know that 20 pounds of meat makes 90 sandwiches.
- First, calculate how many sandwiches can be made with 1 pound of meat:
[tex]\[
\text{Sandwiches per pound} = \frac{90 \text{ sandwiches}}{20 \text{ pounds}} = 4.5 \text{ sandwiches per pound}
\][/tex]
- Now, we need to find out how many pounds of meat are required to make 330 sandwiches:
[tex]\[
\text{Pounds of meat} = \frac{\text{number of sandwiches}}{\text{sandwiches per pound}}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Pounds of meat} = \frac{330 \text{ sandwiches}}{4.5 \text{ sandwiches per pound}} = 73.\overline{3} \text{ pounds} = 73 \frac{1}{3} \text{ pounds}
\][/tex]
Therefore, Derek should buy approximately 73 [tex]\(\frac{1}{3}\)[/tex] pounds of lunch meat for the picnic. This corresponds to the answer option [tex]\( \boxed{73 \frac{1}{3} \text{ pounds}} \)[/tex].
1. Determine the number of sandwiches needed:
- Derek expects that for every 10 people, 11 sandwiches will be consumed.
- There are 300 people attending the picnic.
- To find out how many sandwiches are needed, calculate:
[tex]\[
\text{Number of sandwiches} = \left(\frac{\text{number of people}}{10}\right) \times \text{sandwiches per 10 people}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Number of sandwiches} = \left(\frac{300}{10}\right) \times 11 = 30 \times 11 = 330 \text{ sandwiches}
\][/tex]
2. Determine the amount of lunch meat needed:
- We know that 20 pounds of meat makes 90 sandwiches.
- First, calculate how many sandwiches can be made with 1 pound of meat:
[tex]\[
\text{Sandwiches per pound} = \frac{90 \text{ sandwiches}}{20 \text{ pounds}} = 4.5 \text{ sandwiches per pound}
\][/tex]
- Now, we need to find out how many pounds of meat are required to make 330 sandwiches:
[tex]\[
\text{Pounds of meat} = \frac{\text{number of sandwiches}}{\text{sandwiches per pound}}
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Pounds of meat} = \frac{330 \text{ sandwiches}}{4.5 \text{ sandwiches per pound}} = 73.\overline{3} \text{ pounds} = 73 \frac{1}{3} \text{ pounds}
\][/tex]
Therefore, Derek should buy approximately 73 [tex]\(\frac{1}{3}\)[/tex] pounds of lunch meat for the picnic. This corresponds to the answer option [tex]\( \boxed{73 \frac{1}{3} \text{ pounds}} \)[/tex].
