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.
a. The number of guests you can invite to your party varies inversely with the
price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
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 part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of
these two alleys.
Calculate how many guests you will be able to invite to your party at each of the
bowling alleys. Which alley would you choose for your party? Why?
a. This means that as the price per bowler at the alley decreases, the number of guests you can afford to invite to your party increases. In other words, the more expensive it is per bowler, the fewer guests you can invite, and vice versa.
b. Let's say you are willing to spend $300 to host the bowling party.
c. Let's denote the number of guests you can invite as "n" and the price per bowler as "p." The equation that shows the inverse relationship between the number of guests and the price per bowler can be expressed as:
n = k/p
where "k" is a constant. Given that you are willing to spend $300, we can rewrite the equation as:
n = 300/p
d. Based on research, Bowling Alley A charges $10 per bowler, and Bowling Alley B charges $15 per bowler.
For Bowling Alley A:
n = 300/10
n = 30
For Bowling Alley B:
n = 300/15
n = 20
Therefore, you will be able to invite 30 guests at Bowling Alley A and 20 guests at Bowling Alley B. In this case, you would choose Bowling Alley A because you can invite more guests there, and it aligns with your budget of $300.