In two or more complete sentences write and solve an equation for the situation and explain how you will solve the equation.

 

Fifty students were given a pre and post test for their math course. Overall, most students increased their scores by 20% points. The grades on the post test went up to 95%.  What is the starting range for the grades on the test? 

 
 

Let's denote the initial average test score of the students as \( x \). According to the problem, the students increased their scores by 20 percentage points, so the post-test score can be represented as \( x + 20\% \). We know that the post-test average score was 95%. Therefore, we set up the equation:

\[
x + 20 = 95
\]

**Solving the equation:**
\[
x = 95 - 20 = 75
\]

So, the initial average test score, \( x \), was 75%. This means the starting range for the grades on the test was around 75%.

### Explanation:
- The problem states that the post-test score is 20% higher than the pre-test score.
- We know the post-test score is 95%, so subtracting the 20% increase from 95% gives us the initial score of 75%.

Would you like further details or have any questions?

### Related Questions:
1. If the increase had been 30 percentage points instead of 20, what would the initial score be?
2. What would the post-test score be if the initial score was 70%?
3. How would the initial score change if the increase was 10 percentage points instead of 20?
4. What is the percentage increase if the initial score was 85% and the post-test score is 95%?
5. If the post-test score was 90%, what was the initial score if the increase was 15 percentage points?

### Tip:
When working with percentage increases, always ensure that you correctly add or subtract the percentage from the original value to avoid mistakes.

Fifty students were given a pre and post test for their math course. Overall, most students increased their scores by 20% points. The grades on the post test went up to 95%. What is the starting range for the grades on the test?

Solve the problem of finding the initial test scores of students where the post-test score increased by 20% to reach 95%. This problem explores key concepts of algebra and percentage calculations, making it suitable for students in Grades 6-8.

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