Final answer:
The correct answer is that the possible scores for the next test to maintain an average between 80 and 89 is 52 ≤ x ≤ 95. This range is not reflected in any of the options provided in the question, indicating a possible error in the question's options.
Step-by-step explanation:
To determine the possible scores you could get on your next test in order for your average to be between 80 and 89, we must first calculate the sum of your current test scores and set up a compound inequality. Your current test scores are 93, 69, 89, and 97, which add up to a total of 348. If we denote the score of the next test as x, your new average after five tests will be (348 + x) / 5.
To ensure that your average is at least 80 but no more than 89, we can write the compound inequality 80 ≤ (348 + x) / 5 ≤ 89. We will solve this inequality in two parts:
Therefore, the possible scores for the next test to maintain an average between 80 and 89 is 52 ≤ x ≤ 95. We now compare this range to the options given in the question.
A) 79 < x < 90
B) 80 ≤ x ≤ 89
C) 70 < x < 80
D) 90 < x < 100
None of these options match our calculated range, so it seems like there may be a mistake in the options provided. To address the question accurately based on our calculations, the possible range of scores for the next test should be from 52 to 95, inclusive.