Izzy had an 87 and an 83 on his first two tests and believed that he did well enough on his final exam to keep his B average. However, when he got his grade he received a D. He checked with his instructor and learned that the instructor had made a mistake by transposing the digits when he recorded the final exam grade. If Izzy's incorrect average (mean) for the class was 69 , what was his correct final exam score? Izzy's correct final exam score is (Type a whole number.)

To find Izzy's correct final exam score, we can start by using the information given about his incorrect average. 1. **Calculate the total number of tests**: Izzy has 2 test scores and 1 final exam score, so he has a total of 3 tests. 2. **Calculate the total score based on the incorrect average**: The incorrect average is given as 69. Since there are 3 tests, we can calculate the total score for these tests as follows: \[ \text{Total score} = \text{Average} \times \text{Number of tests} = 69 \times 3 = 207 \] 3. **Calculate the sum of the first two test scores**: Izzy's first two test scores are 87 and 83. We can calculate their sum: \[ \text{Sum of first two tests} = 87 + 83 = 170 \] 4. **Determine the incorrect final exam score**: The incorrect final exam score can be found by subtracting the sum of the first two tests from the total score: \[ \text{Incorrect final exam score} = \text{Total score} - \text{Sum of first two tests} = 207 - 170 = 37 \] 5. **Identify the correct final exam score**: The instructor transposed the digits of the final exam score. Therefore, if the incorrect score is 37, the correct score must be 73 (by reversing the digits). Thus, Izzy's correct final exam score is: \[ \boxed{73} \]