Statement Problem: A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely to the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 20 people go on the trip?
Solution:
Let the cost per person for the bus rental be c;
Let the number of people going on the trip be n;
[tex]c\propto\frac{1}{n}[/tex][tex]\begin{gathered} c=\frac{k}{n} \\ \text{Where k is the constant of proportionality;} \\ k=cn \\ c=30,n=44 \\ k=30\times44 \\ k=1320 \end{gathered}[/tex]Then, we have;
[tex]\begin{gathered} \text{When;} \\ n=20,c=\text{?} \\ c=\frac{k}{n} \\ c=\frac{1320}{20} \\ c=66.00 \end{gathered}[/tex]If 20 people go on the trip, the cost per person is;
[tex]\text{ \$66.00}[/tex]