Your test scores in one class are 81 and 87. What possible scores can you earn on your next test to have a test average between 84 and 99, inclusive?
Your score on the third test must be between
enter your response here and
enter your response here, inclusive.
(Use ascending order.)
To find the possible scores you can earn on your next test, we need to consider the average of the three tests. The average is calculated by adding up the scores of the three tests and dividing by 3.
Let's call the score on the third test "x".
The average of the three tests is: (81 + 87 + x) / 3
We want this average to be between 84 and 99, inclusive.
Setting up the inequality, we have:
84 ≤ (81 + 87 + x)/3 ≤ 99
Multiplying both sides of the inequality by 3 to eliminate the fraction, we get:
252 ≤ 81 + 87 + x ≤ 297
Next, we combine like terms:
252 ≤ 168 + x ≤ 297
Subtracting 168 from all sides, we have:
84 ≤ x ≤ 129
Therefore, the possible scores you can earn on your next test to have a test average between 84 and 99, inclusive, are 84, 85, 86, ..., 129.
To find the range of possible scores on the third test, we need to consider the test average between 84 and 99, inclusive.
First, let's calculate the current average score with the given test scores of 81 and 87. Take the sum of the two scores and divide it by 2 (since there are two tests) to find the average:
(81 + 87) / 2 = 168 / 2 = 84
The current average score is 84.
To find the minimum possible score on the third test, we need to determine the average score if the third test score is at the lowest end of the range, which is 84. We'll assume the third test score is x and use the formula for average:
(81 + 87 + x) / 3 = 84
Simplifying the equation by multiplying both sides by 3:
81 + 87 + x = 252
Combine the known scores:
x = 252 - 81 - 87 = 84
The minimum score on the third test is 84.
To find the maximum possible score on the third test, we need to determine the average score if the third test score is at the highest end of the range, which is 99. Again, we'll assume the third test score is x and use the formula for average:
(81 + 87 + x) / 3 = 99
Simplifying the equation by multiplying both sides by 3:
81 + 87 + x = 297
Combine the known scores:
x = 297 - 81 - 87 = 129
The maximum score on the third test is 129.
Therefore, the possible scores on the third test for a test average between 84 and 99, inclusive, are between 84 and 129, inclusive.
To find out the possible scores you can earn on your next test, let's calculate the minimum and maximum average scores you can achieve.
Minimum average score:
The minimum average score will be calculated using the lowest scores you have earned so far, which are 81 and 87. Assuming you earn the lowest possible score on your third test, the minimum average can be calculated as follows:
(81 + 87 + x) / 3 ≥ 84
Simplifying the equation:
(168 + x) / 3 ≥ 84
168 + x ≥ 252
x ≥ 84
Therefore, the minimum possible score you can earn on your third test is 84.
Maximum average score:
The maximum average score will be calculated using the highest scores you have earned so far, which are 81 and 87. Assuming you earn the highest possible score on your third test, the maximum average can be calculated as follows:
(81 + 87 + x) / 3 ≤ 99
Simplifying the equation:
(168 + x) / 3 ≤ 99
168 + x ≤ 297
x ≤ 129
Therefore, the maximum possible score you can earn on your third test is 129.
So, the possible scores you can earn on your next test to have a test average between 84 and 99, inclusive, are between 84 and 129, inclusive.