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.

How much money are you willing to spend to host this bowling party?
Set up an equation that shows the inverse relationship between the number of guests at your party and the price per bowler.
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?

To figure out how many people you can afford to invite to your bowling party, you need to consider the budget you have set for the party. Let's say you are willing to spend $200 on the party.

To set up an equation that shows the inverse relationship between the number of guests and the price per bowler, you can use the following equation:

Price per bowler = Total cost / Number of guests

Now, you need to research two local bowling alleys to find out the price per bowler at each of them. Let's assume you find the following information:

Bowling Alley A: Price per bowler = $15
Bowling Alley B: Price per bowler = $20

To calculate how many guests you can invite to your party at each of the bowling alleys, plug the respective price per bowler values into the equation and solve for the number of guests:

For Bowling Alley A:
$15 = $200 / Number of guests

Number of guests = $200 / $15
Number of guests ≈ 13.33

So, you can invite approximately 13 guests to your bowling party at Bowling Alley A.

For Bowling Alley B:
$20 = $200 / Number of guests

Number of guests = $200 / $20
Number of guests = 10

So, you can invite 10 guests to your bowling party at Bowling Alley B.

Now, it's time to decide which alley to choose for your party. Based on the calculations, Bowling Alley A allows you to invite more guests (around 13) compared to Bowling Alley B (10), considering your budget of $200.

Therefore, Bowling Alley A would be the better choice for your party, as you can afford to invite more guests while staying within your budget.