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?
Say I'm willing to pay 200 for a party bowling alley a costs 15 a person and b costs 17 a person
a. The statement that the number of guests varies inversely with the price per bowler means that as the price per bowler increases, the number of guests you can invite decreases, and vice versa.
b. I am willing to spend $200 to host this bowling party.
c. Let g represent the number of guests and p represent the price per bowler. The equation to show the inverse relationship between the number of guests and the price per bowler is:
g = kp, where k is a constant. Since I am willing to spend $200, we can write the equation as:
g = 200/p
d. Let's say Bowling Alley A costs $15 per person, and Bowling Alley B costs $17 per person.
For Bowling Alley A:
g = 200/15
g ≈ 13.33
For Bowling Alley B:
g = 200/17
g ≈ 11.76
Based on these calculations, I would choose Bowling Alley A for my party because I would be able to invite around 13 guests as compared to around 11 guests at Bowling Alley B with the same budget of $200.