To find the student's average grade, we first need to determine the total scores and the total weight for both the tests and the quizzes.
Step 1: Calculate the total score for the tests. The test scores are 85 and 92.
\[ \text{Total Test Score} = 85 + 92 = 177 \]
Step 2: Determine the total score for the quizzes. The quiz scores are 82, 75, and 95.
\[ \text{Total Quiz Score} = 82 + 75 + 95 = 252 \]
Step 3: Calculate the total weight of the tests and quizzes. Since each test is worth three times as much as each quiz, we can express the weights as follows:
- Each test has a weight of 3.
- Each quiz has a weight of 1.
Thus, for two tests, the total weight for tests is:
\[ \text{Total Weight for Tests} = 2 \times 3 = 6 \]
And for three quizzes, the total weight for quizzes is:
\[ \text{Total Weight for Quizzes} = 3 \times 1 = 3 \]
Step 4: Calculate the total combined weight. \[ \text{Total Weight} = 6 + 3 = 9 \]
Step 5: Calculate the total weighted score. To find the total weighted score, we combine the weighted test score and quiz score:
\[ \text{Weighted Test Score} = 177 \times 3 = 531 \]
\[ \text{Weighted Quiz Score} = 252 \times 1 = 252 \]
Adding these together gives us the total weighted score:
\[ \text{Total Weighted Score} = 531 + 252 = 783 \]
Step 6: Calculate the average grade. Now, we can calculate the average by dividing the total weighted score by the total weight:
\[ \text{Average Grade} = \frac{\text{Total Weighted Score}}{\text{Total Weight}} = \frac{783}{9} \approx 87 \]
Therefore, the student's average grade is approximately 87.
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