Question
To rent a certain meeting room, a college charges a reservation fee of \( \$ 13 \) and an additional fee of \( \$ 5 \) per hour. The chemistry club wants to spend at most \( \$ 63 \) on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use \( t \) for the number of hours. Write your answer as an inequality solved for \( t \).
Ask by Byrd Floyd. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The possible number of hours \( t \) the chemistry club can rent the meeting room is between 0 and 10 hours, inclusive.
Solution
The cost to rent the room for \( t \) hours is given by the expression
\[
13 + 5t.
\]
We want this cost to be at most \(\$63\):
\[
13 + 5t \le 63.
\]
Subtracting \( 13 \) from both sides, we have
\[
5t \le 50.
\]
Dividing both sides by \( 5 \) gives
\[
t \le 10.
\]
Since the number of hours cannot be negative, we also have
\[
t \ge 0.
\]
Thus, the possible numbers of hours the chemistry club could rent the room satisfy
\[
0 \le t \le 10.
\]
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Simplify this solution Extra Insights
To find the possible number of hours \( t \) the chemistry club could rent the meeting room under the budget constraint, we start by setting up the cost equation based on the given details. The total cost consists of the reservation fee and the hourly charge, which can be expressed as: \[ 13 + 5t \leq 63 \] Now, let's solve the inequality step by step: 1. Subtract the reservation fee from both sides: \[ 5t \leq 63 - 13 \] \[ 5t \leq 50 \] 2. Now, divide both sides by 5: \[ t \leq 10 \] Thus, the inequality solved for \( t \) is: \[ t \leq 10 \] This means the chemistry club can rent the meeting room for up to 10 hours while staying within their budget of \( \$ 63 \).
