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 :
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.
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