Autumn is working two summer jobs, making $16 per hour tutoring and making $12 per hour landscaping. In a given week, she can work no more than 17 total hours and must earn at least $240. If Autumn worked 3 hours landscaping, determine all possible values for the number of whole hours tutoring that she must work to meet her requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.

Question

Gina Santos

Mathematics

22 June, 19:58

Autumn is working two summer jobs, making $16 per hour tutoring and making $12 per hour landscaping. In a given week, she can work no more than 17 total hours and must earn at least $240. If Autumn worked 3 hours landscaping, determine all possible values for the number of whole hours tutoring that she must work to meet her requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.

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Answers (1)

Know the Answer?

Alice Cook · Answer 1

13,14

Step-by-step explanation:

t = tutoring

l = landscaping

16t + 12l ≥240

t+l ≤17

We know that she worked 3 hours landscaping

l = 3

t+3≤17

t ≤14

16t + 12*3 ≥240

16t + 36 ≥240

Subtract 36 from each side

16t ≥204

Divide each side by 16

t ≥204/16

t ≥12.75

We know that

12.75 ≤t≤14

She has to work whole hours

13,14