Final answer:
To solve this problem, use the concept of inverse variation. The price per person is $50 when 14 people want to rent the bounce house.
Step-by-step explanation:
To solve this problem, we need to use the concept of inverse variation. Inverse variation is a relationship between two variables where their product is equal to a constant. Let's denote the price per person as 'p' and the number of people renting the bounce house as 'n'. According to the problem, the price per person varies inversely with the number of people renting the bounce house. This can be represented as a mathematical equation: p = k/n, where 'k' is the constant of variation.
Given that it costs $35 per person when 20 people rent the bounce house, we can substitute the values into the equation to solve for 'k': 35 = k/20. We can rearrange the equation to solve for 'k': k = 35 * 20 = 700.
Now, we can use the value of 'k' to find out the price per person when 14 people want to rent the bounce house. We substitute 'k' and 'n' into the equation: p = 700/14 = $50.