Final answer:
The inequality to represent Joann's situation with the costs of a birthday party at Skate Land is 50 + 5.50x <= 100, where x is the number of people. After solving the inequality, the maximum number of people that can attend the party is 9.
Step-by-step explanation:
To represent Joann's situation with Skate Land's birthday party rental costs, we need to write an inequality considering the flat fee and the per-person charge, as well as Joann's maximum budget. Let x represent the number of people attending the party. The total cost for the number of people is given by the flat fee ($50) plus the per-person charge ($5.50) multiplied by x. Therefore, the inequality would be:
50 + 5.50x ≤ 100
Where:
- 50 is the flat fee for the rental.
- 5.50x represents the total variable cost for x people attending the party.
- 100 is the maximum amount of money Joann is willing to spend.
To solve the inequality:
- Subtract 50 from both sides of the inequality to isolate the variable term:
- Divide both sides by 5.50 to solve for x:
Since Joann can't have a fraction of a person at her party, the maximum number of people that can attend is 9.