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The senior classes at High School A and High School B planned separate trips to the county fair.
The senior class at High School A rented and filled 14 vans and 5 buses with 442 students. High
School B rented and filled 5 vans and 5 buses with 280 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students can a
bus carry?

Respuesta :

Using a system of equations, it is found that:

  • A van can carry 18 students.
  • A bus can carry 38 students.

What is a system of equations?

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 https://brainly.com/question/24342899

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