Kayden is working two summer jobs, making $10 per hour lifeguarding and making $22 per hour tutoring. In a given week, he can work no more than 17 total hours and must earn no less than $290. If Kayden worked 14 hours lifeguarding, determine all possible values for the number of whole hours tutoring that he must work to meet his requirements.
Let's use the variables L for the number of hours lifeguarding and T for the number of hours tutoring.
According to the given conditions:
1. L + T ≤ 17 (total hours should be no more than 17)
2. 10L + 22T ≥ 290 (total earnings should be no less than $290)
Given that Kayden worked 14 hours lifeguarding (L = 14), we can substitute this value into the equations:
1. 14 + T ≤ 17
T ≤ 3
2. 10(14) + 22T ≥ 290
140 + 22T ≥ 290
22T ≥ 150
T ≥ 150/22
T ≥ 6.82
Since Kayden cannot work a fraction of an hour, he must work at least 7 hours tutoring to meet his requirements.