Answer :
To determine how much lunch meat Derek should buy, let's break down the problem step by step:
1. Determine the Total Number of Sandwiches Needed:
- We know that for every 10 people, Derek expects 11 sandwiches to be eaten.
- Since there are 300 people attending the picnic, we need to calculate how many sandwiches will be consumed.
- First, calculate the ratio of sandwiches per person. If 10 people eat 11 sandwiches, it means each person eats 1.1 sandwiches (11 sandwiches / 10 people).
2. Calculate Total Sandwiches for 300 People:
- Multiply the number of sandwiches per person by the total number of people.
- [tex]\( \text{Total sandwiches} = 300 \text{ people} \times 1.1 \text{ sandwiches per person} \)[/tex].
- This results in 330 sandwiches.
3. Determine the Amount of Meat Needed:
- We know that 20 pounds of meat can make 90 sandwiches.
- First, find out how much meat is needed per sandwich: [tex]\( \text{meat per sandwich} = \frac{20 \text{ pounds}}{90 \text{ sandwiches}} \)[/tex].
4. Calculate Total Meat for 330 Sandwiches:
- Multiply the meat needed per sandwich by the total number of sandwiches.
- [tex]\( \text{Meat needed} = 330 \text{ sandwiches} \times \frac{20}{90} \text{ pounds per sandwich} \)[/tex].
- This results in approximately 73.33 pounds of lunch meat.
Therefore, Derek should purchase [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat for the picnic.
1. Determine the Total Number of Sandwiches Needed:
- We know that for every 10 people, Derek expects 11 sandwiches to be eaten.
- Since there are 300 people attending the picnic, we need to calculate how many sandwiches will be consumed.
- First, calculate the ratio of sandwiches per person. If 10 people eat 11 sandwiches, it means each person eats 1.1 sandwiches (11 sandwiches / 10 people).
2. Calculate Total Sandwiches for 300 People:
- Multiply the number of sandwiches per person by the total number of people.
- [tex]\( \text{Total sandwiches} = 300 \text{ people} \times 1.1 \text{ sandwiches per person} \)[/tex].
- This results in 330 sandwiches.
3. Determine the Amount of Meat Needed:
- We know that 20 pounds of meat can make 90 sandwiches.
- First, find out how much meat is needed per sandwich: [tex]\( \text{meat per sandwich} = \frac{20 \text{ pounds}}{90 \text{ sandwiches}} \)[/tex].
4. Calculate Total Meat for 330 Sandwiches:
- Multiply the meat needed per sandwich by the total number of sandwiches.
- [tex]\( \text{Meat needed} = 330 \text{ sandwiches} \times \frac{20}{90} \text{ pounds per sandwich} \)[/tex].
- This results in approximately 73.33 pounds of lunch meat.
Therefore, Derek should purchase [tex]\( 73 \frac{1}{3} \)[/tex] pounds of lunch meat for the picnic.
