Problema Solution
At Susan's auto shop, it takes her 12 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does.
Using the values and variables given, write an inequality describing how many oil changes and tire changes Susan can do in less than 3 hours (180 minutes).
Answer provided by our tutors
The total time that Susan needs to change x oil changes and y tire changes is less than 180 min.
The time needed for x oil changes is 12 * x.
The time needed for y tire changes is 18 * y.
The total time is the sum of the above times and needs to be less than 180 that is
12 * x + 18 * y < 180 divide both sides of equation by 6
12/6 * x + 18/6*y < 180/6
2*x + 3*y < 30
2*x < 30 - 3*y divide both sides by 2 to get the inequality for x
x < 30/2 - 3/2*y = 15 - 1.5 y < 15 that is x < = 15
2*x + 3*y < 30
3*y < 30 - 2*x divide both sides by 3 to get the inequality for y
y < 30/3 - 2/3 *x = 10 - 2/3*x < 10 that is y < = 10
Also we can write x + y < x+ 3/2 * y < 15.
Susan can do not more then 5 oil changes and not more then 10 tire changes or all together she can do not more then 15 total of oil and tire changes.