Question

Write a System of Equations to solve the following problem:

The county 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 13 vans and 2 buses with 211 students. High School B rented and filled 4 vans

and 4 buses with 268 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

#students each VAN can carry:


#students each BUS can carry:

Answer 1

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry: 7

#students each BUS can carry: 60

Explanation:

Let v = number of students in each van.

Let b = number of students in each bus.

High School A:

13v + 2b = 211

High School B:

4v + 4b = 268

The system of equations is

13v + 2b = 211

4v + 4b = 268

We will solve this system of equation with the addition method.

Write the first equation as it is. Divide both sides of the first equation by 2 and write it below the first equation. Then add the equations.

13v + 2b = 211

(+) -2v - 2b = -134

----------------------------

11v = 77

Divide both sides by 11.

v = 7

Substitute 7 for v in the first original equation and solve for b.

13v + 2b = 211

13(7) + 2b = 211

91 + 2b = 211

Subtract 91 from both sides.

2b = 120

Divide both sides by 2.

b = 60

Answer:

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry: 7

#students each BUS can carry: 60

Answer 2

each van carries 7 students

each bus carries 60 students

Explanation:

let v = # students in a van

let b = # students in a bus

system of equations:

13v + 2b = 211

4v + 4b = 268

I multiplied the 1st equation by -2 to eliminate the 'b' terms

-26v - 4b = -422

+ 4v + 4b = 268

-22v = -154

v = 7

substitute '7' for 'v':

4(7) + 4b = 268

28 + 4b = 268

4b = 240

b = 60