Question

Jen’s band is going to record a CD at a recording studio. They will need to pay $225 to rent the studio and $50 per hour for the sound technicians. Jen wants to keep their total cost for recording their CD, between $400 and $500, inclusive.

Write and solve a compound inequality to represent the number of hours x, for which the band can rent the studio.

Answer 1

Jen's band can rent the recording studio for between 3.5 and 5.5 hours, inclusive, in order to keep their total costs between $400 and $500.

Step-by-step explanation:

Jen's band needs to keep their total cost for recording their CD between $400 and $500. The cost to rent the studio is $225, and the cost per hour for sound technicians is $50. We can write a compound inequality to represent the number of hours x they can rent the studio.

The total cost T can be represented as T = $225 + $50x, where x is the number of hours.

To keep the total cost between $400 and $500, inclusive, we have:
400 <= $225 + $50x <= 500

To solve for x, we perform the following steps:

• Subtract $225 from all parts of the inequality:
  175 <= $50x <= 275
• Divide all parts by $50:
  3.5 <= x <= 5.5

Therefore, the band can rent the studio for between 3.5 and 5.5 hours, inclusive.