How many students per van and bus?

Question

This is the question---------- New York is a popular field trip destination. South-West High School and North-West High school both planned trips there. The South-West High School rented and filled 1 van and 6 buses with 324 students. North-West High School rented and filled 9 vans and 3 buses with 264 students. How many students can a van carry? How many students can a bus carry?

Answer 1

Here you have to solve for two different variables using two equations.

v = number of students per van

b = number of students per bus

South-West High School filled 1 van and 6 buses with 324 students:

v + 6b = 324

North-West High School filled 9 vans and 3 buses with 264 students

9v + 3b = 264

Use substitution to solve for one variable. The easiest equation to use is South-West. Isolate v first:

v + 6b = 324

v = -6b + 324

Plug this into North-West equation to solve for b:

9(-6b + 324) +3b = 264

-54b + 2916 + 3b = 264

-51b + 2916 = 264

-51b = -2652

b = 52 students

Then plug this into either equation - South-West is easier.

v + 6(52) = 324

v + 312 = 324

v = 12 students

You can check both equations with these numbers to make sure they are correct.

Answer 2

v + 6b = 324 → v = 324 - 6b

9v + 3b = 264

9(324 - 6b) + 3b = 264

2916 - 72b + 3b = 264

2916 - 68b = 264

-68b = -2652

b = 39

Van you determine the number of vans? (Hint: use the first equation above,)