Question

An outpost has the supplies to last 2 people for 14 days. How many days will the supplies last for 7 people?

• A. 4
• B. 9
• C. 5
• D. 10
• E. 7

Hint:

For inverse proportion problems (\(y \propto 1/x\)), the product of the two quantities is constant (\(k = x \cdot y\)). Here, \(P_1 \times D_1 = P_2 \times D_2\). So, \(2 \times 14 = 7 \times D_2\), which gives \(28 = 7 \times D_2\), and \(D_2 = 4\). This is a quick way to set up and solve such problems.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is an inverse proportion problem. The number of people and the number of days the supplies last are inversely related. This means that if the number of people increases, the number of days the supplies will last must decrease, assuming the consumption rate per person is constant.
Step 2: Key Formula or Approach:
First, calculate the total amount of supplies in "person-days". A "person-day" is the amount of supply one person consumes in one day.
Total Supplies (in person-days) = (Number of people) \(\times\) (Number of days).
Then, find the new number of days by dividing the total supplies by the new number of people.
Days = Total Supplies / New number of people.
Step 3: Detailed Explanation:
Calculate the total supplies available.
\[ \text{Total Supplies} = 2 \text{ people} \times 14 \text{ days} = 28 \text{ person-days} \] This means the outpost has enough supplies to feed one person for 28 days, or 28 people for one day, etc.
Now, we want to find out how long these 28 person-days of supplies will last for 7 people.
\[ \text{Number of days for 7 people} = \frac{\text{Total Supplies}}{\text{Number of people}} \] \[ \text{Number of days} = \frac{28 \text{ person-days}}{7 \text{ people}} = 4 \text{ days} \] Step 4: Final Answer:
The supplies will last for 4 days if there are 7 people.