Question

1. 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.

Explanation:

Step1: Calculate the total of existing scores

The sum of Cindy's existing test scores is \(72 + 82+83 + 89=326\). Let \(x\) be the score on the final exam. Since the final exam counts as two tests, the total number of "test - equivalents" is \(4 + 2=6\).

Step2: Set up the compound inequality for the average

The average formula is \(\text{Average}=\frac{\text{Sum of scores}}{\text{Number of scores}}\). We want \(77\leqslant\frac{326 + 2x}{6}\leqslant84\).
First, multiply each part of the compound inequality by \(6\):
\(77\times6\leqslant326+2x\leqslant84\times6\)
\(462\leqslant326 + 2x\leqslant504\).
Then, subtract \(326\) from each part:
\(462-326\leqslant2x\leqslant504 - 326\)
\(136\leqslant2x\leqslant178\).
Finally, divide each part by \(2\):
\(\frac{136}{2}\leqslant x\leqslant\frac{178}{2}\)
\(68\leqslant x\leqslant89\).

Answer:

Cindy must score between \(68\) and \(89\) (inclusive) on her final exam.