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Pham can work as many or as few hours as she wants at the university bookstore for $9 per hour. But due to her hectic schedule, she has just 15 hours per week that she can spend working either at the bookstore or at other potential jobs. One potential job, at a café, will pay her $12 per hour for up to 6 hours per week. She has another job offer at a garage that will pay her $10 an hour for up to 5 hours per week. And she has a potential job at a daycare centre that will pay her $8.50 per hour for as many hours as she can work. If her goal is to maximize the amount of money she can make each week, how many hours will she work at the bookstore?  hours

Question

Pham can work as many or as few hours as she wants at the university bookstore for 9perhour.Butduetoherhecticschedule,shehasjust15hoursperweekthatshecanspendworkingeitheratthebookstoreoratotherpotentialjobs.Onepotentialjob,atacafeˊ,willpayher9 per hour. But due to her hectic schedule, she has just 15 hours per week that she can spend working either at the bookstore or at other potential jobs. One potential job, at a café, will pay her 12 per hour for up to 6 hours per week. She has another job offer at a garage that will pay her 10anhourforupto5hoursperweek.Andshehasapotentialjobatadaycarecentrethatwillpayher10 an hour for up to 5 hours per week. And she has a potential job at a daycare centre that will pay her 8.50 per hour for as many hours as she can work. If her goal is to maximize the amount of money she can make each week, how many hours will she work at the bookstore?  hours

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Solution

To maximize her weekly earnings, Pham should first consider the jobs that pay her the most per hour.

  1. The café job pays the most at 12perhour,butshecanonlyworkthereforupto6hoursperweek.So,sheshouldworkthefull6hoursatthecafeˊ.Thiswillearnher612 per hour, but she can only work there for up to 6 hours per week. So, she should work the full 6 hours at the café. This will earn her 6 * 12 = $72.

  2. The next highest paying job is at the garage, which pays 10perhourforupto5hoursperweek.Sheshouldworkthefull5hoursatthegarage.Thiswillearnher510 per hour for up to 5 hours per week. She should work the full 5 hours at the garage. This will earn her 5 * 10 = $50.

  3. After working at the café and garage, Pham has worked a total of 6 + 5 = 11 hours. She has 15 - 11 = 4 hours left that she can work in a week.

  4. The bookstore pays more than the daycare centre (9perhourvs9 per hour vs 8.50 per hour), so she should work the remaining 4 hours at the bookstore. This will earn her 4 * 9=9 = 36.

So, Pham will work 4 hours at the bookstore.

This problem has been solved

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