The Seniors of High School A and B

Question

The senior classes at High School A and High School B planned separate trips to the state fair. The senior class at High School A rented and filled 13 Vans and 2 Buses with 181 students. High School B rented and filled 8 Vans and 8 Buses with 328 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?

Answer 1

Hi Nicholas,

This is a system of equations problem. Your two equations would represent High School A and High School B. The two variables (x and y) for both linear equations would represent vans and buses. Lets say that vans represent x and buses represent y (It does not matter if you switch the representation of x and y for buses and vans as long as one variable is x and one variable is y. This means your two equations would be:

A: 13x + 2y = 181

B: 8x + 8y = 328

We can then use elimination to combine equations and eliminate a variable, but first we have to multiply an equation to get a common variable. Since 2 x 4 = 8, it would be the easier to eliminate y by multiplying the top equation by 4. When you multiply one term by 4, you have to multiply everything by 4. The new system would look like:

A: 52x + 8y = 724

B: 8x + 8y = 328 Now we can combine the equations by using subtraction to eliminate y:

44x = 396 Then we would use inverse operations and divide by 44 to solve for x:

x = 9 This means the vans carried 9 students each.

Once we know the answer for the amount of students in one van, we substitute into one of our original equations to solve for the amount of students in a bus:

I am going to use equation B since we did not mess with that equation earlier:

8(9) + 8y = 328

72 + 8y = 328

-72 -72

8y = 256

Then we divide by 8 to solve for y, the amount of students per bus:

256 divided by 8 = 32 students per bus.

Our answer to this system is that 9 students fit in each van (x) and 32 students fit in each bus (y)