Question

In a high school science class, a test is worth three times as much as a quiz. What is the student’s average grade?

Test scores: 85, 92
Quiz scores: 82, 75, 95

Answer 1

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**.