Sofia is working two summer jobs, making $12 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work a maximum of 17 total hours and must earn a minimum of $180. If Sofia worked 14 hours babysitting, determine all possible values for the number of whole hours clearing tables that she must work to meet her requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.

The possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2, 3 hours

Solution:

Amount earned in babysitting = $ 12 per hour

Amount earned in clearing tables = $ 8 per hour

In a given week, she can work a maximum of 17 total hours and must earn a minimum of $180

Sofia worked 14 hours babysitting

Therefore,

Amount earned at babysitting = 14 x 12 = 168

Thus, Sofia earned $ 168 at babysitting

Sofia must earn a minimum of $ 180

Remaining amount to be earned = 180 - 168 = 12

Thus, Sofia must earn $ 12 from clearing tables

Amount earned in clearing tables = $ 8 per hour

So, she must work for atleast 1.5 hours to get $ 12 from clearing tables

She can work a maximum of 17 total hours and Sofia worked 14 hours babysitting

Remaining is 17 - 14 = 3 hours

Thus possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2 hours or 3 hours