So the unified score of 4 tests is calculated so.
)Score1/maxscore1+score2/maxscore2+score3/maxscore3+score4/maxscore4)*40698000.
I want you to calculate the sum of score 1 2 3 and 4 if unified score is 129407856 and max scores are 21 18  17 and 19

To solve for the sum of scores 1, 2, 3, and 4 given the unified score and the maximum scores, we can proceed as follows:

Given:

\[
\text{Unified Score} = \left(\frac{\text{Score}_1}{\text{MaxScore}_1} + \frac{\text{Score}_2}{\text{MaxScore}_2} + \frac{\text{Score}_3}{\text{MaxScore}_3} + \frac{\text{Score}_4}{\text{MaxScore}_4}\right) \times 40698000
\]

We want to find the sum of \(\text{Score}_1 + \text{Score}_2 + \text{Score}_3 + \text{Score}_4\), denoted as \(S_1 + S_2 + S_3 + S_4\).

### Step 1: Calculate the sum of the fractions.

First, rearrange the formula to solve for the sum of the fractions:

\[
\frac{\text{Score}_1}{\text{MaxScore}_1} + \frac{\text{Score}_2}{\text{MaxScore}_2} + \frac{\text{Score}_3}{\text{MaxScore}_3} + \frac{\text{Score}_4}{\text{MaxScore}_4} = \frac{\text{Unified Score}}{40698000}
\]

Substitute the given values:

\[
\frac{\text{Score}_1}{21} + \frac{\text{Score}_2}{18} + \frac{\text{Score}_3}{17} + \frac{\text{Score}_4}{19} = \frac{129407856}{40698000}
\]

### Step 2: Simplify the right side of the equation.

Let's compute this value.The sum of the fractions is approximately \( 3.1797 \).

### Step 3: Express the sum of fractions in terms of scores.

The sum of fractions is:

\[
\frac{\text{Score}_1}{21} + \frac{\text{Score}_2}{18} + \frac{\text{Score}_3}{17} + \frac{\text{Score}_4}{19} \approx 3.1797
\]

To find the sum \( S_1 + S_2 + S_3 + S_4 \), we can multiply each fraction by its respective maximum score and then sum them up. 

\[
S_1 + S_2 + S_3 + S_4 = 21 \times \frac{\text{Score}_1}{21} + 18 \times \frac{\text{Score}_2}{18} + 17 \times \frac{\text{Score}_3}{17} + 19 \times \frac{\text{Score}_4}{19}
\]

Which simplifies to:

\[
S_1 + S_2 + S_3 + S_4 = 21 \times 3.1797
\]

Now, let's compute that.The sum of the scores \( S_1 + S_2 + S_3 + S_4 \) is approximately \( 238.48 \).

### Would you like further details or have any questions?

Here are some related questions for deeper understanding:
1. How can you verify the calculated sum of scores?
2. What would be the effect on the unified score if any of the test scores were maximized?
3. How do different maximum scores impact the unified score?
4. Can this formula be generalized for any number of tests?
5. How would the calculation change if the unified score was given as a percentage?
6. What if one of the maximum scores changes—how would that affect the final sum?
7. How can we reverse the formula to find individual scores if the sum is known?
8. How does rounding impact the final result?

**Tip:** Always double-check your calculations, especially when working with large numbers, to avoid small errors that can lead to significant differences in results.

Learn how to calculate the sum of scores 1, 2, 3, and 4 given the unified score and maximum scores using a detailed step-by-step solution. This problem involves fractional calculations and equations. Suitable for advanced high school students.

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