Math 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 296 students. High School B rented and filled 5 vans

and 3 buses with 141 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?

Answer 1

Let's break this down! The first step of a word problem is to translate the sentences into equations. Let's use "V" to represent vans, and "B" to represent buses.

High School A

The senior class at High School A rented and filled 8 vans and 8 buses with 296 students

8 vans and 8 buses totals 296 students

8V + 8B = 296

High School B

High School B rented and filled 5 vans and 3 buses with 141 students

5 vans and 3 buses totals 141 students

5V + 3B = 141

Next, solve one of the equations for one of the variables (V or B). The equation for High School A looks like a good place to start since each variable is multiplied by the same number (8).

8V + 8B = 296

8V = 296-8B

V = 37 - B

Then, replace V with "37-B" in the other equation for High School B.

5V + 3B = 141

5(37-B) + 3B = 141

Multiply out 5(37-B)

185-5B + 3B = 141

Subtract 185 from each side

-5B + 3B = -44

Combine the terms of B (-5B + 3B)

-2B = -44

Divide both sides of the equation by -2

B = 22

So each bus fits 22 students!

That's one part of the answer. To figure out how many students fit in each van, we can replace "B" with 22 in either of our original equations. Let's use the equation for High School B again:

5V + 3B = 141

5V + 3(22) = 141

5V + 66 = 141

5V = 75

V = 15

So each van fits 15 students.

Here's a way to double check your answer: plug in B=22 and V=15 to one of the original equations. The math should check out. Let's switch things up and use the equation for High School A.

8V + 8B = 296

8(15) + 8(22) = 296 ?

120 + 176 = 296?

296 = 296 Correct!