Question

The state fair 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 4 vans and 2 buses with 104 students. High School B rented and filled 6 vans and 4 buses with 182 students. Each van and each bus carried the same number of students. Find the number of students in each van and in cach bus.

Answer 1

High School A:

4 vans

2 buses

104 students

High school B

6 vans

4 buses

182 students

x = number of studedts carried by each van

y= number of students carried by each bus

We have to write a system of questions:

High school A:

4x+2y = 104 (a)

High school B

6x+4y= 182 (B)

Multiply (a) by 2 and subtract (b) to (a) to eliminate y:

8x +4 y = 208

-

6x+4y= 182

__________

2x = 26

x = 26/2

x= 13

Then, replace x on any initial equation and solve for y:

4(13) +2y= 104

52+2y= 104

2y= 104-52

2y= 52

y= 52/2

y= 26

Number of students in each van=13

Number of students in each bus = 26

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