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Question

At Josh's auto shop, it takes him 9 minutes to do an oil change and 12 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 Josh can do in less than 3 hours ( 180 minutes)

Answer 1

You must set up and inequality equation first. Something like, x+y (>, =, <) z. Then you plug in the rest of what the word problem is asking, x being the amount of oil changes multiplied by 9 and y being the amount of tire changes multiplied by 12 because that is how long it takes for each service to be completed. Finally, you have to finish the inequality by inserting a symbol (>, =, <) and setting "z" equal to 180. You can determine which to use by using the context clues. It says, "... In less than 3 hours..." so you can assume that you will not use the =, or the >, you will use the <. So, it should look something like, 9x + 12y < 180.

 

Hope this helps!!

Answer 2

It will take him 9 minutes to do each of the x oil changes and 12 minutes to do each of the y tire changes. He has 180 minutes AND NO MORE. As an example, if it takes you 10 minutes to read one page in a book, and you wish to read x=6 pages, you can accomplish this in 10*6=60 minutes, so you can read 6 pages in one hour. I hope this is helpful...