Your test scores in one class are 81 and 85. What possible scores can you earn on your next test to have a test average between 83 and 88, inclusive?

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83 <= (81+85+x)/3 <= 88

249 <= 166+x <= 264
Now finish it off

To determine the possible scores you can earn on your next test, we'll use the formula for average:

Average = (Sum of scores) / (Number of scores)

Let's say the score on your next test is x.

To find the possible scores, we'll calculate the range for the sum of scores that will result in an average between 83 and 88 inclusive.

For the lower bound of the range:
83 ≤ ((81 + 85 + x) / 3)
249 ≤ (166 + x)
x ≥ 249 - 166
x ≥ 83

For the upper bound of the range:
((81 + 85 + x) / 3) ≤ 88
(166 + x) ≤ 264
x ≤ 264 - 166
x ≤ 98

Therefore, the possible scores you can earn on your next test to have an average between 83 and 88 inclusive are any scores from 83 to 98 (inclusive).

To find the possible scores you can earn on your next test, we need to consider the average score between 83 and 88.

Let's find the minimum average score first. To get an average of 83, the sum of all three test scores must be 3 * 83 = 249. Since you already have scores of 81 and 85, the sum of your current scores is 81 + 85 = 166. Therefore, you need to score at least 249 - 166 = 83 on your next test to achieve an average of 83.

Now let's find the maximum average score. To get an average of 88, the sum of all three test scores must be 3 * 88 = 264. Since you already have scores of 81 and 85, the sum of your current scores is 81 + 85 = 166. Therefore, you can score at most 264 - 166 = 98 on your next test to achieve an average of 88.

In conclusion, you can score between 83 and 98 on your next test to have a test average between 83 and 88, inclusive.