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Answer :
Sure! Let's solve this step by step:
We need to determine how many days the food, which lasts 54 days for 50 people, will last if there are 60 people.
### Step-by-step Solution:
1. Determine Total Food Supply:
The total amount of food can be considered in "person-days." A "person-day" refers to the amount of food one person would consume in one day. If 50 people have enough food for 54 days, then the total amount of food is:
[tex]\[
\text{Total food in person-days} = 50 \text{ people} \times 54 \text{ days}
\][/tex]
So,
[tex]\[
\text{Total food in person-days} = 2700 \text{ person-days}
\][/tex]
2. Determine Days for New Number of People:
Now, we need to see how long these 2700 person-days of food will last for 60 people. We can divide the total amount of food by the new number of people:
[tex]\[
\text{Days the food will last} = \frac{\text{Total food in person-days}}{\text{Number of people}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Days the food will last} = \frac{2700 \text{ person-days}}{60 \text{ people}}
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Days the food will last} = 45 \text{ days}
\][/tex]
Therefore, the food supply will last for 45 days if there are 60 people in the camp.
We need to determine how many days the food, which lasts 54 days for 50 people, will last if there are 60 people.
### Step-by-step Solution:
1. Determine Total Food Supply:
The total amount of food can be considered in "person-days." A "person-day" refers to the amount of food one person would consume in one day. If 50 people have enough food for 54 days, then the total amount of food is:
[tex]\[
\text{Total food in person-days} = 50 \text{ people} \times 54 \text{ days}
\][/tex]
So,
[tex]\[
\text{Total food in person-days} = 2700 \text{ person-days}
\][/tex]
2. Determine Days for New Number of People:
Now, we need to see how long these 2700 person-days of food will last for 60 people. We can divide the total amount of food by the new number of people:
[tex]\[
\text{Days the food will last} = \frac{\text{Total food in person-days}}{\text{Number of people}}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Days the food will last} = \frac{2700 \text{ person-days}}{60 \text{ people}}
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Days the food will last} = 45 \text{ days}
\][/tex]
Therefore, the food supply will last for 45 days if there are 60 people in the camp.
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