Question

When renting a limo for prom, the number of people is inversely proportional to thecost per person. Originally there were 12 people and the cost per person was $20.If the number of people changed to 3, what would be the new cost per person?

Answer 1

This is an inverse proportionality question, and the relationship between the number of people (say, n) and the cost per person (say, c) can be written as:

`n\text{ }\alpha\text{ }(1)/(c)`

Step 1: Now, we introduce a constant of proportionality as follows:

`n\text{ =k}*\text{ }(1)/(c)`

Step 2: Now, we solve to obtain the value of the constant of proportionality, as follows:

We are given that, originally, there were 12 people and the cost per person was $20.

The above means that, when:

n = 12 , c = $ 20

Now, we substitute for n and c in the proportionality equation as follows:

`\begin{gathered} n\text{ =k}*\text{ }(1)/(c) \\ 12=k*(1)/(20) \\ 12*20=k \\ 240=k \\ k=240 \end{gathered}`

Thus, the constant of proportionality is k = 240

Step 3: Now, we can find the new cost per person (c) if the number of people changed to 3, as follows:

From the proprtionality equation, given as: