Question

Samantha is hosting a birthday celebration in a reception hall that holds at most 144 people. She has arranged tables that can seat 8 people each. A: Create an inequality to solve this problem. B: Identify and explain each part of the inequality in context of the problem.

Answer 1

The inequality to solve Samantha's problem is 8T ≤ 144, where T is the number of tables. Here, 8 represents people per table, ≤ signifies 'at most', and 144 is the hall's capacity.

Step-by-step explanation:

To address Samantha's birthday celebration problem in a reception hall with a maximum capacity of 144 people, we need to create an inequality. Since each table can seat 8 people, let's call the number of tables T. We can then write our inequality as: 8T ≤ 144.

Breaking down the inequality:

The number 8 represents the number of people that can be seated at one table.

The variable T represents the total number of tables that can be set up in the hall.

The operator ≤ is the less than or equal to sign, indicating that the product of 8 people per table and the total number of tables should not exceed the hall's capacity of 144 people.

The number 144 is the maximum number of people that the hall can accommodate.