Question

When renting a limo for prom, the number of people is inversely proportional to the cost per person. Originally there were 6 people and the cost per person was $52. If the number of people changed to 12, what would be the new cost per person?

Answer 1

Given:

Number of people = 6

Cost per person = $52

Let's find the cost per person if the number of people changes to 12.

Given that the number of people is inversely proportional to the cost per person, we have the equation:

`y=(k)/(x)`

Where, k represents the constant of proportionality, y represents the number of people and x represents the cost per person.

Let's find the constant of proportionality k:

`\begin{gathered} 6=(k)/(52) \\ \\ k=6\ast52 \\ \\ k=312 \end{gathered}`

The constant of proportionality, k is 312

To find the cost when number of people changes to 12, we have:

`\begin{gathered} y=(312)/(x) \\ \\ 12=(312)/(x) \\ \\ x=(312)/(12) \\ \\ x=26 \end{gathered}`

Therefore, when the number of people changes to 12, the new cost is $26

ANSWER:

$26