Answer :
Sure, let's solve this step-by-step:
1. Determine the total number of sandwiches needed:
- Derek expects that for every 10 people, 11 sandwiches will be eaten.
- There are 300 people attending the picnic.
- We divide the number of people by 10 to find out how many groups of 10 there are: [tex]\( 300 / 10 = 30 \)[/tex].
- For each group, 11 sandwiches are required. Thus, the total number of sandwiches needed is: [tex]\( 30 \times 11 = 330 \)[/tex].
2. Calculate how many 90-sandwich groups are required:
- 20 pounds of meat will make 90 sandwiches.
- We need a total of 330 sandwiches.
- To find the number of 90-sandwich groups, we divide the total number of required sandwiches by 90: [tex]\( 330 / 90 = 3.6666666666666665 \)[/tex].
3. Calculate the total pounds of meat required:
- Each 90-sandwich group requires 20 pounds of meat.
- We have [tex]\( 3.6666666666666665 \)[/tex] groups.
- Therefore, the total pounds of meat needed is: [tex]\( 3.6666666666666665 \times 20 = 73.33333333333333 \)[/tex].
Converting the decimal to a fraction for clarity:
- [tex]\( 73.33333333333333 \)[/tex] pounds is equivalent to [tex]\( 73 \frac{1}{3} \)[/tex] pounds.
Therefore, Derek should buy [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat. The correct answer is:
[tex]\[ \boxed{73 \frac{1}{3} \text{ pounds}} \][/tex]
1. Determine the total number of sandwiches needed:
- Derek expects that for every 10 people, 11 sandwiches will be eaten.
- There are 300 people attending the picnic.
- We divide the number of people by 10 to find out how many groups of 10 there are: [tex]\( 300 / 10 = 30 \)[/tex].
- For each group, 11 sandwiches are required. Thus, the total number of sandwiches needed is: [tex]\( 30 \times 11 = 330 \)[/tex].
2. Calculate how many 90-sandwich groups are required:
- 20 pounds of meat will make 90 sandwiches.
- We need a total of 330 sandwiches.
- To find the number of 90-sandwich groups, we divide the total number of required sandwiches by 90: [tex]\( 330 / 90 = 3.6666666666666665 \)[/tex].
3. Calculate the total pounds of meat required:
- Each 90-sandwich group requires 20 pounds of meat.
- We have [tex]\( 3.6666666666666665 \)[/tex] groups.
- Therefore, the total pounds of meat needed is: [tex]\( 3.6666666666666665 \times 20 = 73.33333333333333 \)[/tex].
Converting the decimal to a fraction for clarity:
- [tex]\( 73.33333333333333 \)[/tex] pounds is equivalent to [tex]\( 73 \frac{1}{3} \)[/tex] pounds.
Therefore, Derek should buy [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat. The correct answer is:
[tex]\[ \boxed{73 \frac{1}{3} \text{ pounds}} \][/tex]
