1. **State the problem:** We have 15 students with exam scores. The mode and median are both 76, the mean score is 80, and the total score of the 7 lowest-scoring students is 515. We need to find the average score of the remaining 7 students. 2. **Given data:** - Number of students, $n = 15$ - Mode = Median = 76 - Mean score = 80 - Sum of scores of 7 lowest students = 515 3. **Calculate total sum of all scores:** $$\text{Total sum} = \text{mean} \times n = 80 \times 15 = 1200$$ 4. **Median is the 8th score when scores are ordered:** Since median = 76, the 8th score is 76. 5. **Mode is 76, so 76 appears most frequently.** 6. **Sum of scores of 7 highest students:** $$\text{Sum of 7 highest} = \text{Total sum} - \text{Sum of 7 lowest} - \text{Median score}$$ $$= 1200 - 515 - 76 = 609$$ 7. **Average score of the 7 highest students:** $$\text{Average} = \frac{609}{7} = 87$$ **Final answer:** The average score of the remaining 7 students is $87$.