Final answer:
A student can work 32 hours at the Wash Tub to exactly earn the required $256 weekly, working no more than the 40-hour weekly limit. No hours would be needed at Chick-fil-A with this approach, but there's flexibility to work less at the Wash Tub and fill in some hours at Chick-fil-A if desired.
Step-by-step explanation:
Calculating the Work Hours to Meet Financial Needs
Let's solve this problem step-by-step to determine a reasonable amount of hours you can work at both jobs to pay your bills. The student needs to earn at least $256 per week and cannot work more than 40 hours across the two jobs.
First, we will use the equation 6x + 8y = 256 where 'x' is the number of hours worked at Chick-fil-A and 'y' is the number of hours worked at the Wash Tub. The second constraint is to work no more than 40 hours in total; hence x + y ≤ 40.
To maximize the earnings and minimize the working hours, the student should work more hours at the job that pays more, which is the Wash Tub. However, the student must also satisfy the constraints. Let's consider the maximum hours at the Wash Tub, which would be 40 hours. The equation becomes 8 * 40 = 320, which is more than the $256 needed. It means that the student could work fewer hours and still meet their financial needs.
If we try to minimize the hours at the Wash Tub, suppose the student works 32 hours at the Wash Tub, this would yield 8 * 32 = $256, exactly what is needed to pay the bills. This would mean the student works 0 hours at Chick-fil-A, which satisfies both constraints.
In summary, working 32 hours a week at the Wash Tub would earn the student exactly $256 and fulfill the constraint of working no more than 40 hours per week. This seems like a reasonable solution, but the student has the option to work fewer hours at the Wash Tub and some at Chick-fil-A if preferred.