Question

A group of students are going on a field trip. If the group takes 3 vans and 1 car, 22 students can be transported. If the group takes 2 vans and 4 cars, 28 students can be transported. How many students can fit in each van?

Answer 1

6 students in each van.

Explanation:

Having van as x variable and car as y variable.

3x + y = 22

2x + 4y = 28

Step 1: Solve for y in 3x + y =22

y = 22 - 3x

Step 2: Substitute y = 22 - 3x into 2x + 4y =28

2x + 4(22-3x) = 28

2x + 88 - 12x = 28

=> -10x + 88 = 28

Step 3: Solve for x (which is one van) in -10x + 88 = 28,

-10x = 28 - 88

-10x = -60

=> x = 6

Thus, we have 6 students that can fit in each van.

Answer 2

4 cars fit for 12 students. and

2 vans fit for 16 students.