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.
inequality

Answer 1

$400 ≤ $50x + $225 ≤ $500

$175 ≤ $50x ≤ $275

3.5 ≤ x ≤ 5.5

Answer 2

To find the number of hours Jen's band can rent the studio and keep costs between $400 and $500, a compound inequality is created and solved, resulting in a range of 3.5 to 5.5 hours inclusive.

Step-by-step explanation:

The student is asking how to write and solve a compound inequality to represent the number of hours (x) Jen's band can rent the recording studio, keeping their total cost between $400 and $500, inclusive. The fixed cost for renting the studio is $225, and the cost per hour for sound technicians is $50. Therefore, the initial compound inequality based on the given conditions is:

400 ≤ 225 + 50x ≤ 500.

Now, let's solve for x:

1. Subtract 225 from each part of the inequality: 400 - 225 ≤ 50x ≤ 500 - 225.
2. Simplify: 175 ≤ 50x ≤ 275.
3. Divide each part by 50: 175/50 ≤ x ≤ 275/50.
4. Further simplify: 3.5 ≤ x ≤ 5.5.

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