We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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].
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