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

ANSWER

30 students

EXPLANATION

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

Inverse proportion is written as:

$\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \\ \text{where k = constant of proportionality} \end{gathered}$

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:

$\begin{gathered} 250=\frac{k}{24} \\ \Rightarrow k=250\cdot24 \\ k=6000 \end{gathered}$

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

That is:

$\begin{gathered} 200=\frac{6000}{x} \\ \Rightarrow x=\frac{6000}{200} \\ x=30\text{ students} \end{gathered}$

Therefore, 30 students could attend.