Questions: Cindy has scores of 71, 80, 84, and 88 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 70 to 79. A. 13.5 ≤ final score ≤ 36 B. 97 ≤ final score ≤ 151 C. 70 ≤ final score ≤ 79 D. 48.5 ≤ final score ≤ 75.5

Solution Steps

To find the range of scores Cindy can make on her final exam to receive a C, we need to calculate the average of all her test scores, including the final exam which counts as two tests. The average should be between 70 and 79. We will set up a compound inequality to represent this condition and solve for the final exam score.

Cindy's scores on her biology tests are \(71, 80, 84,\) and \(88\). The final exam counts as two tests. We need to find the range of scores she can achieve on her final exam to receive a C, which requires a final course average between 70 and 79.

The average of all test scores, including the final exam counted twice, should satisfy: \[ 70 \leq \frac{71 + 80 + 84 + 88 + x + x}{6} \leq 79 \] where \(x\) is the score on the final exam.

First, multiply the entire inequality by 6 to eliminate the fraction: \[ 70 \times 6 \leq 71 + 80 + 84 + 88 + 2x \leq 79 \times 6 \] This simplifies to: \[ 420 \leq 323 + 2x \leq 474 \]

Subtract 323 from all parts of the inequality: \[ 420 - 323 \leq 2x \leq 474 - 323 \] \[ 97 \leq 2x \leq 151 \]

Divide the entire inequality by 2 to solve for \(x\): \[ \frac{97}{2} \leq x \leq \frac{151}{2} \] \[ 48.5 \leq x \leq 75.5 \]

Final Answer