SOLUTION: There are 20 true/false questions and 20 multiple choice questions on a test. A correct answer to a true false question earns 10 points. A correct answer to a multiple choic

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Question 935100: There are 20 true/false questions and 20 multiple choice questions on a test.
A correct answer to a true false question earns 10 points.
A correct answer to a multiple choice question earns 12 points.
The test makers determined that it takes, on average 3 minutes to answer a true/false question and 4 minutes to answer a multiple choice question. Students have 1 hour to answer to answer at most 18 questions of their choice. How many of each kind of question should a student answer correctly to get the greatest possible score?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There are 20 true/false questions and 20 multiple choice questions on a test.
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A correct answer to a true false question earns 10 points.
A correct answer to a multiple choice question earns 12 points.
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The test makers determined that it takes, on average 3 minutes to answer a true/false question and 4 minutes to answer a multiple choice question.
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Students have 1 hour to answer at most 18 questions of their choice. How many of each kind of question should a student answer correctly to get the greatest possible score?
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t + m <= 18 questions
3t + 4m <= 60 minutes
Objective Rule:: Score = 10t + 12m
t >= 0
m >= 0
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Graph::
t = -m + 18 and shade the area below it in QI
t = (-4/3)m + 20 and shade the area below it in QI
graph%28400%2C400%2C-5%2C40%2C-5%2C30%2C-x%2B18%2C%28-4%2F3%29x%2B20%29
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Find the intercepts and the intersection of the 2 lines.
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(0,18) and (18,0) for t = -m+18
(0,20) and (15,0) for t = (-4/3)m+20
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Find the intersection of the 2 lines:
-m+18 = (-4/3)m + 20
(1/3)m = 2
m = 6 ; and t = -m+18, so t = 12
Intersection:: (6,12)
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Substitute the proper point coordinates into the Objective Function
to determine which combination of t(true/false) and m(multiple choice)
gives a maximum value.
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Cheers,
Stan H.
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