5. cindy has scores of 72, 82, 83, and 89 on her biology tests. use a compound inequality to find the range…
5. 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.
Answer
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.