 The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 6 vans and 4 buses with 214 students. High School B rented and filled 13 vans and 4 buses with 305 students. Every van had the same number of students in it as did the buses. 

There were ______ students in each van.

Let's define the following variables:

- Let \( v \) represent the number of students in each van.
- Let \( b \) represent the number of students in each bus.

We are given the following two pieces of information:

- High School A rented 6 vans and 4 buses, which accommodated 214 students.
  This can be written as the equation: 
  \[
  6v + 4b = 214
  \]

- High School B rented 13 vans and 4 buses, which accommodated 305 students.
  This can be written as the equation:
  \[
  13v + 4b = 305
  \]

### Step 1: Subtract the two equations

To eliminate \( b \), we subtract the first equation from the second:
\[
(13v + 4b) - (6v + 4b) = 305 - 214
\]
Simplifying:
\[
7v = 91
\]

### Step 2: Solve for \( v \)

Now, divide both sides of the equation by 7:
\[
v = \frac{91}{7} = 13
\]

Thus, there were **13 students in each van**.

Would you like to see the steps to find the number of students in each bus?

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Here are 5 follow-up questions to deepen understanding:
1. How many students were in each bus?
2. How many total students could the vans from High School A accommodate?
3. If High School A rented 2 more vans, how many total students would fit?
4. How would the equations change if each bus carried 5 more students?
5. Can we solve this problem if only the total number of students from one school was provided?

**Tip**: When dealing with systems of equations, look for opportunities to eliminate variables by combining the equations.

The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 6 vans and 4 buses with 214 students. High School B rented and filled 13 vans and 4 buses with 305 students. Every van had the same number of students in it as did the buses. There were ______ students in each van.

Discover how to solve a real-world systems of linear equations problem where two high schools rent vans and buses for their senior class trips. Learn the step-by-step solution to find the number of students in each van, using algebraic elimination. Suitable for Grades 8-10.

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