At a school camp there is enough food for 150 students for 5 days.
a How long would the food last if there were
only 100 students?
b If the food ran out after only 4 days, how many
students attended the camp?

Let's solve these problems step by step.

### a) How long would the food last if there were only 100 students?

We know that the food is enough for 150 students for 5 days. The total amount of food available can be thought of as \( 150 \times 5 = 750 \) student-days. This means that the food can support 1 student for 750 days.

If there are 100 students, we need to find how many days \( x \) the food will last.

The total number of student-days would still be the same (750), so we set up the equation:

\[
100 \times x = 750
\]

Solving for \( x \):

\[
x = \frac{750}{100} = 7.5 \text{ days}
\]

So, the food would last for 7.5 days if there were only 100 students.

### b) If the food ran out after only 4 days, how many students attended the camp?

Let \( n \) be the number of students who attended the camp. We know the food can last for 750 student-days, and it ran out after 4 days. This means:

\[
n \times 4 = 750
\]

Solving for \( n \):

\[
n = \frac{750}{4} = 187.5
\]

Since the number of students must be a whole number, we round to the nearest whole number:

\( n = 188 \).

So, 188 students attended the camp.

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Do you want more details or have any questions? 

Here are 5 related questions to expand on this topic:

1. If 200 students attended the camp, how many days would the food last?
2. What would happen if the number of students increased by 50 each day?
3. If the food lasted for 10 days, how many students were there initially?
4. How would the food supply change if each student needed twice as much food?
5. If 120 students attended for the first 3 days and then 180 for the next 2 days, how long would the food last?

**Tip:** In word problems involving proportions, setting up equations based on "total work" or "total consumption" often makes the problem easier to solve.

Explore solutions to school camp food problems involving student numbers and days. Learn how to calculate food duration for different student counts and scenarios. Suitable for Grades 5-6.

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