Rahul is working two summer jobs, making $13 per hour tutoring and making $9 per hour clearing tables. In a given week, he can work at most 14 total hours and must earn no less than $170. If Rahul worked 10 hours clearing tables, determine the minimum number of whole hours tutoring that he must work to meet his requirements.
Let x be the number of hours Rahul works tutoring.
Since he worked 10 hours clearing tables, he has 14 - 10 = 4 hours left to work.
His total earnings must be at least $170, so we have the inequality:
13x + 9(10) ≥ 170
13x + 90 ≥ 170
13x ≥ 80
x ≥ 80/13
Since x must be a whole number, the minimum number of whole hours tutoring that he must work is 7.