a. An inverse relationship between the number of guests and the price per bowler means that as the price per bowler increases, the number of guests you can invite decreases. Conversely, as the price per bowler decreases, the number of guests you can invite increases.
b. Let's say you're willing to spend $200 on the bowling party.
c. Let x be the number of guests you can invite, and y be the price per bowler. Then the inverse relationship can be represented by the equation xy = k, where k is a constant. Solving for x, we get x = k/y. Substituting the value of k with the given budget of $200, we get x = 200/y.
d. Let's say Bowling Alley A charges $10 per bowler, and Bowling Alley B charges $12 per bowler.
Using the equation from part (c), we can calculate the maximum number of guests we can invite at each alley:
- Bowling Alley A: x = 200/10 = 20 guests
- Bowling Alley B: x = 200/12 ≈ 16.67 guests
Based on these calculations, we can invite more guests to Bowling Alley A than Bowling Alley B. Therefore, we would choose Bowling Alley A for our party.
Task 3
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?
1 answer