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satela [25.4K]
3 years ago
8

A student earns $10 per hour for tutoring and $7 per hour as a teacher's aide. To have enough free time for studies, he can work

no more than 20 hours per week. The tutoring center requires that each tutor spends at least three hours per week tutoring, but no more than eight hours per week. How many hours should he work to maximize his earnings?
hours of tutoring hours as a teacher's aide What is the maximum profit? $
Mathematics
1 answer:
gavmur [86]3 years ago
5 0
Since he gets paid more for tutoring, he should work as many hrs tutoring as possible. He can only work at most 20 hrs. He has to work at least 3 hrs tutoring but no more then 8 hrs.....to maximize profit, he needs to work 8 hrs tutoring...leaving 12 hrs as a teachers aide. He should work 20 hrs to maximize his earnings.

maximum profit is : 8(10) + 12(7) = 80 + 84 = 164




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Answer:

a)

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Now we know that Gavin also gives a $3 tip, so we need to add this to the cost:

c(m) = ($0.65*m + $7) + $3 = $0.65*m + $10

c(m) = $0.65*m + $10

Now we know that he paid a total of $62.65

Then:

c(m) = $62.65 =  $0.65*m + $10

This is the equation we need to solve in order to find m, the number of miles between Gavin's house and the airport.

b)

$62.65 =  $0.65*m + $10

We only need to isolate m, we will get:

$62.65 - $10 =   $0.65*m

$52.65/$0.65 =  m = 81

This means that there are 81 miles between the airport and Gavin's house.

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