Thursday, September 5, 2013

Percent word problems -- set one


Percent word problems  -- set one.

Background:

Students unfamiliar with the concept of percentage may want to go to the Khan web site and watch some videos on percentages.   The links below should help students find pertinent material.




Students unfamilar with the average may want to go the following Khan video.
http://www.khanacademy.org/math/probability/descriptive-statistics/central_tendency/v/mean-median-and-mode

After watching these videos the student would turn to this problem.

Questions:  

A student has taken three tests.  Scores on the tests were 83 correct out of 100, 84 correct out of 100, and 79 out of 100.    The student has one more test, a final exam.

What is the student’s percent correct prior to taking the final exam?

Assume the final exam is also 100 points.  What is the lowest percent correct the student can get and still have 80% correct for the semester?

Is it possible for the student to get more than 90% correct if the final exam is worth 100 points?

Assume the final exam is 200 points.  What is the lowest percent correct the student can get on the final and still have 80% for the semester?  

Is it possible for the student to get 90% for the semester if the final is 200 points?

Answers:  

What is the percent correct over the first three exams?

The percent correct on the first three tests is 100*((83+84+79)/300) or 100*246/300, which is 82.0%.


Based on a 100 point final what is the lowest score that will keep the student over 80% for the semester?

B is the number correct out of 100 problems on the final   The fraction correct for the entire semester is  (B+246)/400.  Set this fraction equal to 0.80.  

0.80=(B+246)/400

this simplified to 

0.80 x 400 = (B+246)

or 

B= (0.80 x 400-246) = 74

With 74 correct on the final exam the student will have exactly  80% correct for the semester. Note (74+246)/400 is 0.80.  

Can the student get to 90% for the semester if there are only 100 problems on the final exam?


The highest possible final fraction correct is (100+246)/400 or 346/400 or 0.865.  
This is 86.5%.    The student will not get to 90.0% if the exam is only worth 100 points.

What is the lowest percent correct the student can get on a 200 problem final exam and still remain above 80%?

B is the number correct.   The fraction correct is (B+246)/500.  Setting this fraction equal to 0.80

0.80 x 500 = (B+246)

Solving for B we get

B=(0.80 x 500-246) = 154 


The student must get 154 out of 200 correct to remain at 80.0% correct or better.  (154 out of 200 is 77.0%)

Can the student get to 90.0% for the semester if there is a 200 point final exam?


The highest possible percent correct for the semester based on a 200 point final  is

100x(246+200)/(500) or 89.2%.

At this point in the semester 90.0% is not attainable even if the final exam is worth 200 points.

Percent word problem set two will be available soon.  When it is available I will place the link here.


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