SOLUTION: A student received scores of 84, 73, and 71 on their midterm algebra exams. If the final exam counts twice as much as a midterm, what score must the student make on their final exa

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Question 1203603: A student received scores of 84, 73, and 71 on their midterm algebra exams. If the final exam counts twice as much as a midterm, what score must the student make on their final exam to get an average score of 80? (Assume that the maximum possible score on each test is 100.)
Found 3 solutions by Edwin McCravy, greenestamps, josgarithmetic:
Answer by Edwin McCravy(20054) About Me  (Show Source):
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I've never heard of a class having three midterm exams. But who knows what some
teachers do. 

I assume we add the three midterm scores once each and the final score, X, twice,
as though the final exam score were 2 midterm exams, and find the average as
though there were 5 separate midterm exams.

%2884%2B73%2B71%2BX%2BX%29%2F5%22%22=%22%2280

Simplify and solve for X.

Edwin

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor shows a standard method for solving a problem like this regarding averages.

If the numbers in the problem are all close together, as they are in this problem about test scores, then often a faster path to the answer is to compare each of the scores to the desired average.

In this problem...
84 is +4 compared to the desired average
73 is -7 compared to the desired average
71 is -9 compared to the desired average

The three tests together are +4-7-9 = -12 compared to the desired average.

The final exam is worth twice as much as each midterm; to make up the shortage of 12 points from the three midterms, the score on the final must be 6 points over the desired average.

ANSWER: 80+6 = 86

CHECK: (84+73+71+2(86))/5 = 400/5 = 80

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
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A student received scores of 84, 73, and 71 on their midterm algebra exams.
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Is this one student or ("their") more than one student?
Are these scores all in one single course? One student taking three different "Midterm Tests" in one course during the same term(semester) makes no sense.