We can solve this by setting up a proportion based on the given ratio of teachers to students.

The ratio is:

$\frac{3 \text{ teachers}}{50 \text{ students}}$

Now, we want to find how many teachers are needed for 2,650 students, so let $x$ represent the number of teachers required:

$\frac{x \text{ teachers}}{2650 \text{ students}} = \frac{3 \text{ teachers}}{50 \text{ students}}$

To solve for $x$, we can cross-multiply:

$50x = 3 \times 2650$

Now calculate:

$50x = 7,950$

Now, divide by 50:

$x = \frac{7,950}{50} = 159$

So, 159 teachers are needed for 2,650 students.

Would you like more details or have any questions?

Here are 5 related questions for you:

1. What would be the number of students if there were 200 teachers?
2. How many teachers are needed for 5,000 students?
3. If the number of students increases by 500, how many additional teachers are required?
4. If there were 6 teachers for every 50 students, how many teachers would be needed for 2,650 students?
5. How would the ratio change if the number of students per teacher was reduced to 40?

Tip: Ratios can be scaled up or down proportionally to find equivalent values.