Suppose you are having a birthday party at the local bowling alley. You are trying to figure out how many people you can afford to invite.
b. How much money are you willing to spend?
c. Set up an equation that shows the inverse relationship between the number of guests at your party and the price per bowler. Your answer to part b should be a part of this equation.
My answer for part b is $100 and I understand what the question in asking for as well as what an inverse variation is, however, how would I start setting up this equation?
guests * price = k
for some constant k.
To set up the equation that represents the inverse relationship between the number of guests at your party and the price per bowler, you can start by assigning variables to the different quantities involved.
Let's use:
- x to represent the number of guests at the party
- y to represent the price per bowler
Since the number of guests and the price per bowler have an inverse relationship, we can say that as the number of guests increases, the price per bowler decreases, and vice versa.
Now, using the information given in part b, which is $100, we can assume that you are willing to spend $100 in total, and this amount should cover the cost for all the bowlers.
To calculate the total cost, we can multiply the number of guests (x) by the price per bowler (y), which gives us the equation:
Total cost = x * y
In this case, the total cost should be equal to $100, so we have:
Total cost = $100
Plugging in the equation for the total cost, we get:
x * y = $100
This equation represents the inverse relationship between the number of guests (x) and the price per bowler (y), with the total cost being $100. You can use this equation to determine the number of guests you can afford to invite within your budget.