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.
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.
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