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.
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