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# Basic Math/Inequalities

Question
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.

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.

Abe

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

Basic Math

Volunteer

#### Abe Mantell

##### Expertise

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!

##### Experience

Over 15 years teaching at the college level.

Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

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