Question
Ella’s test grades in her history class are 89, 94, 82, 84, and 98. What score must Ella make on her next test to have a mean test score of 90?
needed on the next test
needed on the next test
Answers
GPT-4o mini
To find out what score Ella needs on her next test to have a mean score of 90, we first need to calculate the total score she needs after all her tests, including the next one.
1. **Calculate the mean**: The mean \( M \) is calculated using the formula:
\[
M = \frac{\text{Total of all test scores}}{\text{Number of tests}}
\]
In this case, if Ella takes \( n+1 \) tests in total (where \( n \) is the number of tests she has taken so far), we want:
\[
90 = \frac{\text{Sum of current test scores} + \text{Next test score}}{n + 1}
\]
2. **Calculate the sum of current test scores**: First, we find the sum of her current test scores.
- The current scores are: 89, 94, 82, 84, and 98.
- Calculate the sum:
\[
89 + 94 + 82 + 84 + 98 = 447
\]
3. **Determine the total test count**: She has taken 5 tests, so the number of tests after the next one will be 6.
4. **Set up the equation**: We set up the equation for the mean:
\[
90 = \frac{447 + x}{6}
\]
(where \( x \) is the score she needs on the next test).
5. **Solve for \( x \)**: Multiply both sides by 6 to eliminate the fraction:
\[
540 = 447 + x
\]
Now, isolate \( x \):
\[
x = 540 - 447
\]
\[
x = 93
\]
Therefore, Ella needs to score **93** on her next test to achieve a mean test score of 90.
1. **Calculate the mean**: The mean \( M \) is calculated using the formula:
\[
M = \frac{\text{Total of all test scores}}{\text{Number of tests}}
\]
In this case, if Ella takes \( n+1 \) tests in total (where \( n \) is the number of tests she has taken so far), we want:
\[
90 = \frac{\text{Sum of current test scores} + \text{Next test score}}{n + 1}
\]
2. **Calculate the sum of current test scores**: First, we find the sum of her current test scores.
- The current scores are: 89, 94, 82, 84, and 98.
- Calculate the sum:
\[
89 + 94 + 82 + 84 + 98 = 447
\]
3. **Determine the total test count**: She has taken 5 tests, so the number of tests after the next one will be 6.
4. **Set up the equation**: We set up the equation for the mean:
\[
90 = \frac{447 + x}{6}
\]
(where \( x \) is the score she needs on the next test).
5. **Solve for \( x \)**: Multiply both sides by 6 to eliminate the fraction:
\[
540 = 447 + x
\]
Now, isolate \( x \):
\[
x = 540 - 447
\]
\[
x = 93
\]
Therefore, Ella needs to score **93** on her next test to achieve a mean test score of 90.