Allowing each soldier five ounces of protein each day, an army of 600 soldiers has enough provisions for five weeks. With the same total amount of provisions, how many soldiers could be fed for 10 weeks if each soldier receives only three ounces of protein per day?

To solve this problem, we need to determine the total amount of protein available and then figure out how many soldiers can be fed for 10 weeks with a reduced daily protein allowance. We will follow these steps:

1. Calculate the total amount of protein available for the original 600 soldiers over 5 weeks.
2. Calculate the total number of soldier-days that this amount of protein can support if each soldier receives 3 ounces of protein per day.
3. Determine how many soldiers can be fed for 10 weeks with the same total amount of protein.

**Step 1: Calculate the total amount of protein available**

Each soldier receives 5 ounces of protein per day. The total protein required per day for 600 soldiers is:
\[
600 \text{ soldiers} \times 5 \text{ ounces/soldier/day} = 3000 \text{ ounces/day}
\]

The total amount of protein for 5 weeks (where 1 week = 7 days) is:
\[
3000 \text{ ounces/day} \times 5 \text{ weeks} \times 7 \text{ days/week} = 105000 \text{ ounces}
\]

**Step 2: Calculate the total number of soldier-days supported**

With the total protein available being 105000 ounces, and each soldier receiving 3 ounces per day, the total number of soldier-days that can be supported is:
\[
\frac{105000 \text{ ounces}}{3 \text{ ounces/soldier/day}} = 35000 \text{ soldier-days}
\]

**Step 3: Determine how many soldiers can be fed for 10 weeks**

We need to find the number of soldiers (\(N\)) that can be supported for 10 weeks. The number of days in 10 weeks is:
\[
10 \text{ weeks} \times 7 \text{ days/week} = 70 \text{ days}
\]

The number of soldiers \(N\) that can be supported for 70 days is:
\[
N \times 70 \text{ days} = 35000 \text{ soldier-days}
\]
\[
N = \frac{35000 \text{ soldier-days}}{70 \text{ days}} = 500 \text{ soldiers}
\]

Therefore, with the same total amount of provisions, 500 soldiers can be fed for 10 weeks if each soldier receives only 3 ounces of protein per day.

Would you like further details or have any questions?

Here are 5 questions you might ask next:
1. How can the calculation be adjusted for different daily protein allowances?
2. What other factors might affect the provisions calculation in real scenarios?
3. How would you handle calculations for different types of provisions?
4. Can you explain the concept of "soldier-days" in more detail?
5. What strategies can be used to optimize provisions for longer periods?

**Tip:** When solving problems involving provisions or resources over time, breaking down the problem into daily usage and total available units can simplify the calculations.

Learn how to calculate the number of soldiers that can be fed with specific protein rations over different time durations. This problem involves proportional reasoning and unit conversion, suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation