Question

At Ahmad's auto shop, it takes him 9 minutes to do an oil change and 15 minutes to do a tire change. Let x be the number of oil changes he does. Let y be the number of tire changes he does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Ahmad can do in less than 3 hours (180 minutes).

a) 9x + 15y < 180
b) 15x + 9y < 180
c) 9x - 15y < 180
d) 15x - 9y < 180

Answer 1

The inequality that represents how many oil changes (x) and tire changes (y) Ahmad can perform in less than 3 hours is (a) 9x + 15y < 180, as it takes him 9 minutes per oil change and 15 minutes per tire change. Therefore, the correct answer is (a) 9x + 15y < 180.

Step-by-step explanation:

The question asks for an inequality that describes how many oil changes and tire changes Ahmad can do in less than 3 hours, which is 180 minutes. Since it takes Ahmad 9 minutes to perform an oil change, and 15 minutes to complete a tire change, we assign 'x' for the number of oil changes and 'y' for the number of tire changes. Therefore, the time taken for 'x' oil changes is 9x minutes, and the time taken for 'y' tire changes is 15y minutes.

To ensure that the combined time for both services is less than 3 hours, the total time spent, which is 9x minutes for oil changes plus 15y minutes for tire changes, should be less than 180 minutes. Thus, the correct inequality would be:

9x + 15y < 180

Therefore, the correct answer is (a) 9x + 15y < 180.