Use an algebraic approach to solve the problem. Aura took three biology exams and has an average score of 85. Her second exam score was 6 points better than her first, and her third exam score was 1 point better than her second exam. What were her three exam scores? \( \square \) (lowest score) (highest score)

Sure, let's solve the problem step-by-step using an algebraic approach. ### **Problem Statement** - **Average Score:** Aura has an average of 85 across three biology exams. - **Second Exam:** Her second exam score was 6 points better than her first. - **Third Exam:** Her third exam score was 1 point better than her second exam. We need to find: 1. **Lowest Score** (First Exam) 2. **Highest Score** (Third Exam) ### **Step 1: Define Variables** Let's assign variables to each of Aura's exam scores: - Let \( x \) be the score of the **first exam** (lowest score). - Then, the **second exam** score is \( x + 6 \). - The **third exam** score is \( (x + 6) + 1 = x + 7 \). ### **Step 2: Set Up the Equation** Given that the **average** of the three exams is 85, the **total** of all three scores is: \[ \text{Total} = 3 \times 85 = 255 \] So, we can write the equation: \[ x + (x + 6) + (x + 7) = 255 \] ### **Step 3: Simplify and Solve for \( x \)** Combine like terms: \[ 3x + 13 = 255 \] Subtract 13 from both sides: \[ 3x = 255 - 13 \] \[ 3x = 242 \] Divide both sides by 3: \[ x = \frac{242}{3} \] \[ x = 80.\overline{6} \] \[ x \approx 80.67 \] ### **Step 4: Find the Other Scores** Now that we have \( x \), we can find the other two scores. - **Second Exam:** \[ x + 6 = 80.67 + 6 = 86.67 \] - **Third Exam:** \[ x + 7 = 80.67 + 7 = 87.67 \] ### **Final Answers** - **Lowest Score (First Exam):** \( \boxed{80.67} \) - **Highest Score (Third Exam):** \( \boxed{87.67} \) --- **Note:** If exam scores are typically whole numbers, it's possible that there might be rounding involved or the original problem expects fractional scores. However, based on the given information, the scores are approximately 80.67, 86.67, and 87.67.