A fort has enough provision for its 250 soldiers for 10 weeks. If another 100 soldiers join then, how long will the provisions last?

The problem involves provisions for soldiers, and we can solve it by using the concept of proportionality.

We know:
- The fort has provisions for **250 soldiers for 10 weeks**.
- Another **100 soldiers** join, making a total of **250 + 100 = 350 soldiers**.

Since the total amount of provisions is fixed, the number of soldiers is inversely proportional to the number of weeks the provisions will last. Thus, if more soldiers are added, the provisions will last for fewer weeks.

Let \( x \) represent the number of weeks the provisions will last for **350 soldiers**.

Using the inverse proportionality relation:

\[
250 \times 10 = 350 \times x
\]

Solving for \( x \):

\[
x = \frac{250 \times 10}{350} = \frac{2500}{350} = \frac{2500}{350} = \frac{25}{3} \approx 8.57
\]

Thus, the provisions will last approximately **8.57 weeks**, or about **8 weeks and 4 days**.

### Would you like more details or have any other questions?

#### Related Questions:
1. If 50 more soldiers joined after 3 weeks, how long would the remaining provisions last?
2. If provisions were increased by 20%, how long would they last with 350 soldiers?
3. How many soldiers could the provisions sustain for 12 weeks?
4. If the soldiers consumed provisions at a rate of 5% less per week, how long would they last for 350 soldiers?
5. What would happen if the provisions were cut by half while still maintaining 350 soldiers?

#### Tip:
In proportionality problems, always remember to account for changes in the factor that affects the outcome, such as the number of soldiers in this case.

Solve the provisions problem: If a fort has enough provision for 250 soldiers for 10 weeks, how long will the provisions last if 100 more soldiers join? This problem covers the concept of inverse proportionality and is suitable for students in Grades 6-8.

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