Word Problem

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 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

Answer 1

Hello Chris, I'm going to use V for van, and B for bus. You may anticipated that this is a linear system or 2 equations with 2 unknowns. I'm going to use substitution (vs. elimination) to solve.

 

Equation School A:

8V + 8B = 240    (I'm always tempted to reduce, but not necessary. You could divide both sides by 8.

Equation School B:

4V + B = 54    (I'm using this to substitute because B is easy to isolate)

B = 54 - 4V to be substituted in to School B's equation 

 

So...

8V + 8 (54 - 4V) = 240

8V + 432 - 32V = 240 by distributing

-24V = -192 by...come on it's May. we can combine V terms and subtract 432 in one step

divide both sides by -24

V=8

 

To find B, you can substitute this V into either equation (which I always recommend to check), but I'll use the one that's already ready for us. B = 54 - 4(8) = 54-32=22

B=22

 

Good luck, TV