Using a system of equations, it is found that:
- A van can carry 18 students.
- A bus can carry 38 students.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given by:
- Variable x: Number of students that a van can carry.
- Variable y: Number of students that a bus can carry.
A rented and filled 14 vans and 5 buses with 442 students, hence:
14x + 5y = 442.
High School B rented and filled 5 vans and 5 buses with 280 students, hence:
5x + 5y = 280.
Simplifying by 5:
x + y = 56.
y = 56 - x.
Hence:
14x + 5(56 - x) = 442.
9x = 162
x = 162/9
x = 18.
Then:
y = 56 - x = 56 - 18 = 38.
Hence:
- A van can carry 18 students.
- A bus can carry 38 students.
More can be learned about a system of equations at brainly.com/question/24342899
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