The number of classrooms (C) in Roque School t years from now can be modeled by the
equation C(t) = 400 + 25t. The number of students (S) in each classroom also increases
with time, which can also be modeled by the equation S(t) = 25 + t. Write a formula for
the total number of students in Roque School t years from now.

To find the total number of students in Roque School \( t \) years from now, we need to multiply the number of classrooms by the number of students per classroom. Given the equations:

- \( C(t) = 400 + 25t \) (number of classrooms)
- \( S(t) = 25 + t \) (number of students per classroom)

The total number of students \( T(t) \) in Roque School is the product of these two expressions:

\[
T(t) = C(t) \times S(t)
\]

Substitute the expressions for \( C(t) \) and \( S(t) \):

\[
T(t) = (400 + 25t) \times (25 + t)
\]

Now, expand this product:

\[
T(t) = 400 \times (25 + t) + 25t \times (25 + t)
\]

\[
T(t) = 400 \times 25 + 400 \times t + 25t \times 25 + 25t \times t
\]

\[
T(t) = 10000 + 400t + 625t + 25t^2
\]

Combine like terms:

\[
T(t) = 25t^2 + 1025t + 10000
\]

So, the formula for the total number of students in Roque School \( t \) years from now is:

\[
T(t) = 25t^2 + 1025t + 10000
\]

Would you like more details on the steps, or do you have any questions?

Here are some related questions:
1. What is the total number of students after 5 years?
2. How many classrooms will there be after 10 years?
3. What happens to the total number of students if the increase in students per classroom changes?
4. How does the total number of students grow after 20 years?
5. What is the number of students in each classroom after 15 years?

**Tip:** Always check that units match when combining mathematical models in real-world applications (e.g., classrooms and students per classroom).

The number of classrooms (C) in Roque School t years from now can be modeled by the equation C(t) = 400 + 25t. The number of students (S) in each classroom also increases with time, which can also be modeled by the equation S(t) = 25 + t. Write a formula for the total number of students in Roque School t years from now.

Explore how the number of students in Roque School increases over time using algebraic models for classrooms and students per classroom. Learn how to find the total number of students using the formula T(t) = 25t^2 + 1025t + 10000. Ideal for students in Grades 9-11 studying quadratic equations and algebraic modeling.

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