Question

The cost per student of a ski trip varies inversely as the number of students who attend. It will cost each student $250 if 24 students attend. How many students would have to attend to get the cost down to $200?

Answer 1

30 students

Step-by-step explanation

The cost per student varies inversely as the number of students.

Inverse proportion is written as:

`\begin{gathered} y\propto(1)/(x) \\ y=(k)/(x) \\ \text{where k = constant of proportionality} \end{gathered}`

Let the cost per student be y.

Let the number of students be x.

It will cost each student $250 if 24 students attend. This means that:

`\begin{gathered} 250=(k)/(24) \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}`

If the cost is down to $200, it means that y is now $200.

That is:

`\begin{gathered} 200=(6000)/(x) \\ \Rightarrow x=(6000)/(200) \\ x=30\text{ students} \end{gathered}`

Therefore, 30 students could attend.