Math Problem Performance Task

Question

A High School is taking the Senior Class to Florida for their senior trip. They are covering the costs for transportation for students and teachers to travel by buses and vans.  

Additional Information:

Each bus holds 52 students and teachers at a cost of $1200 each. Each van holds 25 students and teachers at a cost of $700 each. There are a total of 491 students and teachers. There are 5 more buses than vans.

How much money will the High School have to provide to cover the cost of the buses and vans?

Answer 1

Hi Nina!

The best way to solve these questions is to assign assign a variable to each piece we're looking for. First let's figure out how many buses and vans we need. Let's call Vans = V and Buses = B. We don't need to assign teachers and students a variable because we know there are 491 total and in this case the problem doesn't differentiate between them.

So the statements made about Vans and Buses "There are 5 more buses than vans." gives us the equation:

B = V + 5

and the statement about the cost, which we can call C, gives us:

C = B*$1200 + V*$700

We know that Buses can hold 52 students/teachers, and vans hold 25. The total number of students and teachers we need to carry are at minimum 491. From this, we can write the inequality:

B*52 + V*25 ≥ 491

This is a two variable equation, which has infinite solutions, but with the nice equation we came up with earlier we can substitute it in for B to get an equation with only one variable:

(V + 5)*52 + V*25 ≥ 491

Which we can simplify:

V*52 + 260 + V*25 ≥ 491

V*77 + 260 ≥ 491

V*77 ≥ 231

V ≥ 231/77

V ≥ 3

If we had gotten an answer like V ≥ 3.2 , since we can't have a fraction of a van, we would have needed to round up to 4. Since we got a nice round 3, though, we don't need to do any rounding and we can carry on. Now that we know we have 3 vans, we know that we have 8 buses because of our earlier equation relating B and V. Now we can calculate the cost, our cost equation from the price of buses and vans provided:

C = V*700 + B*1200

And we can plug in our numbers and get the following:

C = 3*700 + 8*1200 = 11,700

So our answer is $11,700.