In a study camp, food is available for 45 days for 50 students. For how many days will this food be sufficient for 90 students? 

To solve this problem, we can use the concept of the inverse relationship between the number of students and the number of days the food will last.

Given:
- Food is sufficient for 45 days for 50 students.

We need to find out how many days (\(x\)) the food will last for 90 students.

### Step-by-Step Solution

1. **Total amount of food available**:
   - If 50 students can be fed for 45 days, then the total "student-days" worth of food is \( 50 \times 45 = 2250 \) student-days.
   
2. **New number of students**:
   - The food now needs to be distributed among 90 students.

3. **Determine the number of days**:
   - Let \( x \) be the number of days the food will last for 90 students.
   - The total "student-days" for the new scenario will be \( 90 \times x \).

4. **Set up the equation**:
   \[
   90 \times x = 2250
   \]

5. **Solve for \( x \)**:
   \[
   x = \frac{2250}{90} = 25
   \]

### Answer:
The food will be sufficient for 25 days for 90 students.

Would you like a detailed breakdown of this method or have any questions?

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**Related Questions**:
1. If 30 students were present, for how many days would the food last?
2. What happens if 100 students are present? How many days will the food last?
3. If the number of students increased to 75, how many days would the food supply last?
4. What would happen if 60 students are present instead of 90? How many days will the food last?
5. If the camp received extra food that increased the total amount by 50%, how many days will it last for 90 students?

**Tip**: Remember that when resources are fixed, increasing the number of people using those resources will decrease the duration they last, and vice versa.

Learn how to calculate the sufficiency of food for 90 students from an initial supply meant for 50 students over 45 days. This problem involves understanding inverse proportionality in mathematics, applicable for students in Grades 7-9.

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