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Basic Math/Inequalities


Hi Abe, I am stuck on this question and have the answer, but I don't know what are the steps to get to it... Can you please help me? I have  copy of it below;

Cindy has scores of 72, 82, 83, and 89 on her biology tests. Use a compound inequality to find the range of scores she can make on her final exam to receive a C in the course. The final exam counts as two tests, and a C is received if the final course average is from 77 to 84.

Thank you.

Hello Adrian,

Let x=the final exam score.

Thus, her average will be: (72+82+83+89+2x)/6, divide by 6 since the final counts
as two tests.  Simplifying gives: (326+2x)/6, which needs to be greater than or equal
to 77 and less than or equal to 84.  Which can be written as:
77 <= (326+2x)/6 <= 84, multiply through by 6 to get
462 <= 326+2x <= 504, now subtract 326 from each to get
136 <= 2x <= 178, now divide through by 2 to get
68 <= x <= 89

Thus, Cindy needs any score from 68 through 89.


BTW: Odd that a grade from 80 to 84 is a "C" instead of a "B."  :-o

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Abe Mantell


Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!


Over 15 years teaching at the college level.

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B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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