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?
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.
a. When it is said that the number of guests you can invite to your party varies inversely with the price per bowler at the alley, it means that as the price per bowler increases, the number of guests you can afford to invite decreases. In other words, as the cost per person rises, you will be able to invite fewer people.
b. To determine how much money you are willing to spend to host the bowling party, you need to establish a budget. This budget will depend on factors such as your financial situation, how much you're willing to allocate for the party, and any other expenses you may have.
c. Let's assume that the number of guests at your party is represented by "g" and the price per bowler is represented by "p." The equation that shows the inverse relationship between the number of guests and the price per bowler is:
g = k/p
Where "k" is a constant factor. In this case, "k" would represent the total budget or the maximum number of guests you can afford at a certain price per bowler. So, the equation can be rewritten as:
g = k/p
d. Researching two local bowling alleys will give you the price per bowler at each of these alleys. Once you have the prices, you can substitute them into the equation to find out how many guests you can afford to invite at each alley.
Let's say the price per bowler at Alley A is $10 and at Alley B is $15. Assuming a budget of $200, we can calculate the number of guests at each alley:
At Alley A:
g = 200/10
g = 20 guests
At Alley B:
g = 200/15
g ≈ 13.33 guests
Based on these calculations, you would be able to invite more guests (20) to your party at Alley A as compared to Alley B (13.33). Therefore, Alley A would be the preferable choice for your party because it allows you to invite more people within your budget.