Question

a small auditorium can seat 320 people. which inequality best represents the number of people, p, who can sit in the auditorium? p < 319 p > 320 p > 319 p < 321

Explanation:

Step1: Understand the problem

The auditorium can seat 320 people, so the number of people \( p \) must be less than or equal to 320, or equivalently, \( p \) can be at most 320. We can also think of it as \( p \) is less than 321 (since \( p \leq 320 \) implies \( p < 321 \) when \( p \) is a whole number representing people).

Step2: Analyze each option

• Option 1: \( p < 319 \) would mean the auditorium can seat less than 319 people, which is not true as it can seat 320.
• Option 2: \( p > 320 \) would mean more than 320 people can sit, but the auditorium can only seat 320, so this is false.
• Option 3: \( p > 319 \) would mean more than 319 people, but it doesn't cap at 320 (it would allow more than 320), so this is incorrect.
• Option 4: \( p < 321 \) means the number of people is less than 321, which is equivalent to \( p \leq 320 \) (since the number of people is a non - negative integer), and this correctly represents the number of people that can sit in the auditorium (from 0 up to 320).

Answer:

\( p < 321 \) (the fourth option)