Question Video: Writing and Evaluating a Linear Function in a Real-World Context Mathematics • 8th Grade

Video Transcript

A school organized a trip where there is a fixed cost of 317 pounds and the rest of the cost is dependent on the number of students attending. The total cost for a trip with 35 students is 597 pounds. Find the total cost of the trip for 60 students given the relationship between the total cost and the number of students is linear.

When we look to solve this problem, we first of all look and we see that actually it says that the relationship between the total cost and the number of students is a linear one. So therefore, we can actually set up a linear equation to help us actually find out how much the total cost of the trip for 60 students is going to be.

And the equation that is formed is this one. We’ve got 𝐶𝑇 equals 𝐶𝐹 plus 𝑆 multiplied by 𝑥, where 𝐶𝑇 is the total cost, 𝐶𝐹 is the fixed cost, 𝑆 is the number of students, and 𝑥 is the cost per student. Okay, great, so now we have our equation, we can now actually go on and solve to find the cost of the trip to 60 students.

However, before we can actually find out the cost for 60 students, we first will have to find out the cost for a student. And to do that, we’re gonna look at the trip for 35 students because we have all the information from that one. And that way, we can calculate the cost per student.

First of all, we have 𝐶𝑇 because the total cost for the trip for 35 students is 597 pounds. Then, we have 𝐶𝐹 is equal to 317 because the fixed cost is 317 pounds. 𝑆 is equal to 35 cause there are 35 students. And 𝑥 actually well, we don’t know what 𝑥 is because that’s the cost per student — that’s what we’re trying to find.

So now, all we have to do is substitute our values in and solve for 𝑥. So we get 597 equals 317 plus 35𝑥. And then, we subtract 317 from each side, which gives us 280 is equal to 35𝑥. And then, finally, we divide by 35. So we get eight is equal to 𝑥 or 𝑥 is equal to eight. So therefore, we know that the cost per student is eight pounds.

So now, we can get on and solve the problem and try and find the total cost of the trip for 60 students. So therefore, 𝐶𝑇 is our unknown because that’s what we’re trying to find. 𝐶𝐹 is 317 because that’s still our fixed costs. So that’s the same as before. This time 𝑆 is equal to 60 because as we said there are 60 students. And then, finally, 𝑥 is equal to eight because we actually calculated that previously. So we found the cost per student is eight pounds.

Okay, great, so now we’ve got these, we can actually substitute them in and find our total cost for 60 students. So therefore, we can say that 𝐶𝑇, our total cost, is equal to 317 plus eight multiplied by 60, which is equal to 317 plus 480, which gives us a total of 797.

So therefore, we can say that the total cost for the trip for 60 students is 797 pounds.