### 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.