A student scored 69 points on his Psychology 101 midterm. If the average of his midterm and final must be between 78 and 90 inclusive for a B, then for what range of scores on the final exam would a student get a B? Both tests have a maximum of 100 points. Hint: Write a compound inequality-with his average between 78 and 90 inclusive.

To determine the range of final exam scores that would result in a **B** for the student, we'll follow these steps: 1. **Understand the Requirements:** - **Midterm Score:** 69 points - **Final Exam:** Maximum of 100 points - **Average Needed for a B:** Between 78 and 90 (inclusive) 2. **Set Up the Compound Inequality:** The average of the midterm and final exam scores should be between 78 and 90. This can be expressed as: \[ 78 \leq \frac{\text{Midterm} + \text{Final}}{2} \leq 90 \] 3. **Plug in the Midterm Score:** \[ 78 \leq \frac{69 + \text{Final}}{2} \leq 90 \] 4. **Multiply All Parts by 2 to Eliminate the Fraction:** \[ 156 \leq 69 + \text{Final} \leq 180 \] 5. **Subtract 69 from All Parts to Solve for the Final Exam Score:** \[ 87 \leq \text{Final} \leq 111 \] 6. **Consider the Maximum Possible Score:** Since the final exam is out of 100 points, the upper limit of 111 is not possible. Therefore, the final exam score must be **no more than 100**. 7. **Final Range:** \[ 87 \leq \text{Final} \leq 100 \] **Conclusion:** To achieve a **B**, the student must score **at least 87** points on the final exam and **no more than 100** points. **Answer:** All final exam scores from 87 through 100 are eligible for a B.