Your test scores in one class are 83 and 89. What possible scores can you earn on your next test to have a test average between 86 and 90 inclusive.
To find the possible scores you can earn on your next test, we need to calculate the average including the scores 83, 89, and the next test score.
Let's say the next test score is represented by x.
The average including these three scores is: (83 + 89 + x)/3.
To have an average between 86 and 90 inclusive, we can set up the following inequality:
86 ≤ (83 + 89 + x)/3 ≤ 90.
Let's solve this inequality.
Multiplying both sides of the inequality by 3, we get:
258 ≤ 83 + 89 + x ≤ 270.
Combining like terms, we have:
258 ≤ 172 + x ≤ 270.
Subtracting 172 from all sides, we get:
86 ≤ x ≤ 98.
Therefore, the possible scores you can earn on your next test to have a test average between 86 and 90 (inclusive) are any score between 86 and 98, including both endpoints.
To find the possible scores you can earn on your next test, we need to determine the range of values that will give you a test average between 86 and 90 inclusive.
The average is calculated by summing all the test scores and dividing by the total number of tests.
Let's assume there have been "n" tests and the next test is the "nth+1" test.
To have an average between 86 and 90 inclusive, we can set up the following inequality:
(83 + 89 + x) / (n + 1) ≥ 86 and (83 + 89 + x) / (n + 1) ≤ 90
Now, let's solve the first inequality:
(83 + 89 + x) / (n + 1) ≥ 86
(83 + 89 + x) ≥ 86(n + 1)
83 + 89 + x ≥ 86n + 86
x ≥ 3n + 3
Next, let's solve the second inequality:
(83 + 89 + x) / (n + 1) ≤ 90
(83 + 89 + x) ≤ 90(n + 1)
83 + 89 + x ≤ 90n + 90
x ≤ 90n + 18
Therefore, the possible scores you can earn on your next test are any values of x that satisfy the inequality:
3n + 3 ≤ x ≤ 90n + 18
Please note that without knowing the value of "n" (the number of previous tests taken), we cannot provide specific values for the possible scores on your next test. By plugging in the value of "n," you can find the corresponding range of possible scores.
To determine the possible scores you can earn on your next test, we need to find the range of test scores that will give you a test average between 86 and 90 (inclusive). Let's break it down step by step:
1. Calculate the current average of your test scores by adding them together and dividing by the total number of scores. In this case: (83 + 89) / 2 = 86.
2. To find the upper and lower limits for a test average between 86 and 90 (inclusive), we'll start with the upper limit. Subtract the current average from the desired maximum average to find the maximum score you can earn on the next test: 90 - 86 = 4.
3. To find the lower limit, subtract the desired minimum average from the current average. In this case: 86 - 86 = 0.
4. Your possible scores on the next test fall within the range of 0 to 4 to achieve a test average between 86 and 90 (inclusive).
Therefore, you can earn any score between 0 and 4 on your next test to have a test average between 86 and 90 (inclusive).