Word Problem

Question

The senior class at High School A and High School B planned separate trips to the county Fair. The senior class at High School A rented and filled 1 van and 1 bus with 34 students. High school B rented and filled 1 van and 10 buses with 250 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?

 

a. Van:10, bus 24

b.Van: 15, Bus 27

c. Van 13, Bus 31

d. Van 6, Bus 13

Answer 1

The answer is A

Let  V = van capacity

Let B = Bus Capacity

 

We have the following parallel equations based on the description of how many were filled. (note that this would be much more complex but more likely  situation where vans or buses were partially filled).

 

1. V+B = 34

2. V + 10*B = 250

 

Lets used equation #1 to express B as a function of V

B = 34 - V

 

Now we can replace B in equation 2 with an expression of V. this will simplify equation 2 to an equation with one unknown.

V + 10(34-V) = 250

V + 340-10V = 250

-9V + 340 = 250

-9V = =90

9V = 90

V = 10

 

Now, we plug the value V into our simplified equation 1 to get

B = 34-10

B = 24