Deepa is working two summer jobs, making $6 per hour walking dogs and making $10 per hour clearing tables. In a given week, she can work no more than 12 total hours and must earn no less than $80. If Deepa worked 7 hours clearing tables, determine all possible values for the number of whole hours walking dogs that she must work to meet her requirements.
Let x be the number of hours Deepa works walking dogs.
Given that Deepa can work no more than 12 hours in a week, the total number of hours she works is x + 7.
The total amount she earns in a week is 6x + 10(7) = 6x + 70.
According to the requirement, she must earn no less than $80, so:
6x + 70 ≥ 80
6x ≥ 10
x ≥ 10/6
x ≥ 5/3
Since x must be a whole number, the only possible value for x is 2.
Therefore, Deepa must work 2 hours walking dogs in order to meet her requirements.