Sally plans to go on vacation next summer. She can work no more than 41 hours each week at her two jobs. Tutoring 5th graders pays her $5 per hour, and baking cakes pays $8 per hour. She needs at least $755 for her ticket to Guyana.

Let `c` represent the number of hours she works at the bakery per week.
Let `t` represent the number of hours she tutors per week.

If Sally wants to save money for her ticket in 10 weeks, how many hours should she work at the bakery, and how many hours should she tutor each week?

Question

04-12-2023
Mathematics

High School

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Sally plans to go on vacation next summer. She can work no more than 41 hours each week at her two jobs. Tutoring 5th graders pays her $5 per hour, and baking cakes pays $8 per hour. She needs at least $755 for her ticket to Guyana.

Let `c` represent the number of hours she works at the bakery per week.
Let `t` represent the number of hours she tutors per week.

If Sally wants to save money for her ticket in 10 weeks, how many hours should she work at the bakery, and how many hours should she tutor each week?

Answer :

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t3211628 t3211628 · Answer 1 · 2024-07-17T16:45:01-04:00

Final answer:

To achieve her goal in a 10 week time frame, Sally should work 33 hours each week at the bakery and tutor for 8 hours.

Explanation:

This is a problem of linear algebra, which can be solved using a system of linear equations. Sally can work no more than 41 hours in a week, so this sets up our first equation: c + t = 41, where 'c' and 't' are the hours Sally works at the bakery and as a tutor respectively.

We also know that Sally needs to accumulate at least $755 in 10 weeks, which means she needs to make a minimum of $75.5 per week: 5t (tutoring income) + 8c (baking income) = 75.5, which builds our second equation.

The solution to these two equations will give Sally the optimal numbers of hours she should spend on each job. Simple linear algebra leads us to c = 33 (bakery) and t = 8 (tutoring). Therefore, Sally should ideally work 33 hours at the bakery and 8 hours as a tutor each week to meet her goal.

Learn more about Linear Algebra here:

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