Question

Jenna's band is going to record a CD at a recording studio. They will pay $225 to use the studio for one day and $80 per hour for sound technicians. Jenna has $205 and can reasonably expect to raise up to an additional $350 by taking pre-orders for the CDs.

*"n" represents the number of hours in the studio
I also need to know: Jenna's band is willing to spend between $205 and $555. So, the total cost 225 + 80n must be in this range. The inequality that models this is ?≤ 225 + 80n ≤?

Answer 1

To find the inequality representing the possible total costs for Jenna's band to record in a studio, we begin with the inequality 205 ≤ 225 + 80n ≤ 555. After isolating the variable term and simplifying, we arrive at -0.25 ≤ n ≤ 4.125, with the valid range of hours being 0 to 4.125 since negative hours are not possible.

Step-by-step explanation:

The question is asking to find an inequality that represents the range of possible total costs for recording a CD at a studio, where there is a fixed cost and a variable cost per hour. Jenna's band is willing to spend a minimum of $205 and a maximum of $555 on recording. The total cost of using the studio is the fixed cost of $225 plus $80 per hour for sound technicians, which is represented by the variable n in the inequality.

To model this situation, we set up the inequality: 205 ≤ 225 + 80n ≤ 555. This reads as: the total cost (225 + 80n) must be greater than or equal to 205 and less than or equal to 555.

First, we can subtract 225 from all parts of the inequality to isolate the variable term on one side: -20 ≤ 80n ≤ 330. Then, to solve for n, we divide each part of the inequality by 80, resulting in: -0.25 ≤ n ≤ 4.125. However, since n represents hours, and we cannot have a negative number of hours, the practical range for n is 0 to 4.125 hours.