Question

You are planning a skating party at a rink that charges a basic fee of $5.50 and $7.00 per person for catered parties. You don't want to spend more than $103.50. Write and solve an inequality to find the number of people who can attend the party.

Answer 1

To find the number of people who can attend the party, write and solve the inequality: $5.50 + $7.00x ≤ $103.50. Divide both sides of the inequality by $7.00 to solve for 'x'. The number of people who can attend the party is at most 14.

Step-by-step explanation:

To find the number of people who can attend the party, we need to set up an inequality based on the given information. Let's assume that the number of people who attend the party is 'x'. The basic fee is $5.50, so the cost of the party without any additional charges would be $5.50. For catered parties, the cost is $7.00 per person. Therefore, the total cost of the party would be $5.50 + $7.00x. We also know that the total cost cannot exceed $103.50. So we can write the inequality as:

$5.50 + $7.00x ≤ $103.50

To solve this inequality, we need to isolate 'x' on one side:

$7.00x ≤ $103.50 - $5.50

$7.00x ≤ $98.00

To solve for 'x', divide both sides of the inequality by $7.00:

x ≤ $98.00 / $7.00

x ≤ 14

So the number of people who can attend the party is at most 14.