There are enough resources for 24 employees for 50 days. When would the similar resources last, if there were 15 employees?

The problem is about inverse proportionality: fewer employees would make the resources last longer and vice versa. Let's solve it step by step.

We are given:

- Resources for 24 employees last for 50 days.
- We need to find how long the same resources would last for 15 employees.

We can set up the relation:

\[
\text{Number of employees} \times \text{Days resources last} = \text{Constant}
\]

So, for the first case:

\[
24 \times 50 = \text{Constant}
\]

Now, for the second case with 15 employees, we know the constant is the same:

\[
15 \times \text{Days} = 24 \times 50
\]

Solving for the number of days the resources would last for 15 employees:

\[
15 \times \text{Days} = 1200
\]

\[
\text{Days} = \frac{1200}{15} = 80 \text{ days}
\]

So, the resources would last for **80 days** if there were 15 employees.

Would you like more details or have any other questions?

Here are 5 related questions to explore further:

1. What if the number of employees changes to 30? How long would the resources last?
2. How does this problem change if the resources decrease by half?
3. If 10 employees are added halfway through the 50 days, how many total days would the resources last?
4. Can you generalize a formula for different numbers of employees?
5. What would happen if the employees work at different rates of resource consumption?

**Tip:** In inverse proportion problems, as one quantity increases, the other decreases proportionally.

Solve the inverse proportionality problem: If resources last 50 days for 24 employees, how long would they last for 15 employees? This problem explores key algebraic concepts like inverse proportionality and provides a step-by-step solution. Suitable for Grades 6-8.

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