Lily wants to start tutoring after school and babysitting for families in her neighborhood. She wants to...

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Lily wants to start tutoring after school and babysitting for families in her neighborhood. She wants to spend between 4 and 9 hours per week babysitting. She can work a maximum of 25 hours per week. Lily charges $10 per hour for babysitting and $15 per hour for tutoring. How many hours should Lily work at each job to earn the maximum amount possible?

SnapAndSolve AI · Accepted Answer

Let x be the number of hours spent babysitting and y be the number of hours spent tutoring.

We have the following constraints:

4 ≤ x ≤ 9
x + y ≤ 25

We want to maximize the earnings: 10x + 15y.

To maximize earnings, Lily should maximize the hours spent on the higher-paying job, which is tutoring at $15 per hour. Therefore, she should minimize babysitting hours to 4 (the minimum allowed) and maximize tutoring hours.

Substitute x = 4 into the constraint x + y ≤ 25:

4 + y ≤ 25

y ≤ 21

Thus, Lily should work 4 hours babysitting and 21 hours tutoring to maximize her earnings.

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