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
To find the score on the third test that would give an average between 84 and 99, we need to calculate the average of the current scores and set up an equation.
The average of the current scores is equal to (81 + 87)/2 = 84.
If we let x represent the score on the third test, the average including the third test score is (81 + 87 + x)/3.
To find the range of possible scores for the third test, we need to solve the following inequality:
84 ≤ (81 + 87 + x)/3 ≤ 99
Multiplying all terms by 3 to remove the denominator:
252 ≤ 81 + 87 + x ≤ 297
Combining like terms:
252 ≤ 168 + x ≤ 297
Subtracting 168 from all terms:
84 ≤ x ≤ 129
Therefore, the possible scores on the third test that would give an average between 84 and 99, inclusive, are between 84 and 129.
To determine the possible scores you can earn on your next test, we need to calculate the minimum and maximum average scores based on the given information.
1. Minimum Average Score:
To calculate the minimum average score, we assume that your next test score is the minimum possible score in the inclusive range (84). We add up your current test scores (81 + 87) and the assumed minimum score (84) and divide it by the total number of tests (3).
Minimum Average Score = (81 + 87 + 84) / 3
2. Maximum Average Score:
To calculate the maximum average score, we assume that your next test score is the maximum possible score in the inclusive range (99). We add up your current test scores (81 + 87) and the assumed maximum score (99) and divide it by the total number of tests (3).
Maximum Average Score = (81 + 87 + 99) / 3
Now, we have the range of possible average scores. We need to find the range of scores on the third test that would result in an average between the previously calculated minimum and maximum averages.
Range of scores on the third test = (Minimum Average Score * 3) - (81 + 87), (Maximum Average Score * 3) - (81 + 87)
Substituting the values:
Range of scores on the third test = (Minimum Average Score * 3) - 168, (Maximum Average Score * 3) - 168
Therefore, the possible scores on your next test to have a test average between 84 and 99, inclusive, must be between:
(Minimum Average Score * 3) - 168 and (Maximum Average Score * 3) - 168.
To find the range of possible scores for the third test, we can use the formula for average:
Average = (Sum of all scores) / (Number of scores)
In this case, we have two known scores (81 and 87) and we want the average to be between 84 and 99, inclusive. Let's denote the score on the third test as "x".
1. Calculate the lower average:
Lower Average = (81 + 87 + x) / 3
We want the lower average to be at least 84:
(81 + 87 + x) / 3 ≥ 84
2. Solve for x:
81 + 87 + x ≥ 252
x ≥ 252 - 81 - 87
x ≥ 84
So, the minimum possible score on the third test is 84.
3. Calculate the upper average:
Upper Average = (81 + 87 + x) / 3
We want the upper average to be at most 99:
(81 + 87 + x) / 3 ≤ 99
4. Solve for x:
81 + 87 + x ≤ 297
x ≤ 297 - 81 - 87
x ≤ 129
So, the maximum possible score on the third test is 129.
Therefore, the score on the third test must be between 84 and 129, inclusive.