Please answer algebra word problem

Question

The senior classes at High School A and High School B planned separate trips to the local amusement park. The senior class at High School A rented and filled 12 vans and 11 buses with 429 students. High School B rented and filled 4 vans and 1 bus with 71 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

a. Define variables:

b. System:

c. Solve the systems (optional):

Answer 1

Let x = number of students a van holds

y = number of students a bus holds

For School A we get the equation 12x + 11y = 429

For School A we get the equation 4x + y = 71

Our system of equations will be:

12x + 11y = 429

4x + y = 71

To solve this system of equations, let's use the elimination method. So we multiply each term in the bottom equation by 11 so we can eliminate y.

12x + 11y = 429

44x + 11y = 781

Now we subtract the equations and get:

-32x = -352

x = 11

Now we substitute 11 for x in one of our equations:

4(11) + y = 71

44 + y = 71

y = 27

So a van holds 11 students, and a bus holds 27

Answer 2

Let v = the # of students per van and b = the # of students per bus.

12v + 11b = 429

4v + b = 71

b = 71 - 4v

12v + 11(71 - 4v) = 429

12v + 781 - 44v = 429

-32v = -352

v = 11 students

b = 71 - 4(11)

b = 71 - 44

b = 27 students