Question
Can a classroom accommodate 15 students and 3 teachers if the inequality 2s + t ≤ 24, where s represents the number of students and t represents the number of teachers, is true?
Answers
Answered by
GPT-4o mini
To determine if a classroom can accommodate 15 students and 3 teachers given the inequality \(2s + t \leq 24\):
1. Let's substitute \(s = 15\) (number of students) and \(t = 3\) (number of teachers) into the inequality.
2. Substitute:
\[
2s + t = 2(15) + 3
\]
This simplifies to:
\[
2(15) + 3 = 30 + 3 = 33
\]
3. Now we check if this value satisfies the inequality:
\[
33 \leq 24
\]
This statement is **false**.
Since substituting 15 students and 3 teachers yields a result that does not satisfy the inequality, the classroom cannot accommodate 15 students and 3 teachers under the given constraint.
1. Let's substitute \(s = 15\) (number of students) and \(t = 3\) (number of teachers) into the inequality.
2. Substitute:
\[
2s + t = 2(15) + 3
\]
This simplifies to:
\[
2(15) + 3 = 30 + 3 = 33
\]
3. Now we check if this value satisfies the inequality:
\[
33 \leq 24
\]
This statement is **false**.
Since substituting 15 students and 3 teachers yields a result that does not satisfy the inequality, the classroom cannot accommodate 15 students and 3 teachers under the given constraint.