Answer:
band could rent room B for a maximum of 9.44 hours.
Explanation:
To represent the time (in hours) the band could rent room A, we need to consider both the cleaning fee and the hourly rate. The total cost of renting room A for t hours is given by the expression "50 + 24t". Since the band has $250 to spend, we can write an inequality to represent the maximum time they could rent the room:
50 + 24t <= 250
We can solve this inequality for t by subtracting 50 from both sides:
24t <= 200
Then, by dividing both sides by 24, we get:
t <= (200/24) hours
t <= 8.33 hours
So, the band could rent room A for a maximum of 8.33 hours.
b. To represent the time (in hours) the band could rent room B, we can use a similar approach as above. The total cost of renting room B for t hours is given by the expression "80 + 18t". Using the same budget of $250, we can write the following inequality:
80 + 18t <= 250
We can solve this inequality for t by subtracting 80 from both sides:
18t <= 170
Then, by dividing both sides by 18, we get:
t <= (170/18) hours
t <= 9.44 hours
So, the band could rent room B for a maximum of 9.44 hours.
c. From the above results, we can see that the band could rent room B for a slightly longer period of time compared to room A. However, the hourly rate for room B is cheaper than that of room A. So even though the band will get to use room B for a longer period of time, they will pay less overall to rent it. Additionally, the cleaning fee is cheaper in room B. Based on this information, the band should rent room B. They can stay in the room longer, pay less per hour, and pay less in cleaning fees.