Question

at her auto shop, debra does oil changes and tire changes. the table below shows how long (in minutes) it takes her to complete each of these services.
| time to complete each service (in minutes) |

oil change	12
tire change	24

let x be the number of oil changes she does.
let y be the number of tire changes she does.
suppose debra works for less than 60 minutes. using the values and variables given, write an inequality describing this.

Explanation:

Step1: Determine time for each service

Oil change takes 12 minutes per job, so for \( x \) oil changes, time is \( 12x \) minutes. Tire change takes 24 minutes per job, so for \( y \) tire changes, time is \( 24y \) minutes.

Step2: Total time and inequality

Total time is \( 12x + 24y \). Debra works less than 60 minutes, so \( 12x + 24y < 60 \). (We can simplify by dividing by 12: \( x + 2y < 5 \), but the basic inequality from total time is \( 12x + 24y < 60 \).)

Answer:

\( 12x + 24y < 60 \)