Your test scores in one class are 84 and 88

What possible scores can you earn on your next test to have a test average between 86 and 90 ​inclusive?

86 < (84+88+x)/3 < 90

258 < 84+88+x < 270
86 < x < 98

To find the possible scores you can earn on your next test, we need to consider the test average range of 86 to 90 inclusive.

Let's assume the score on your next test is 'x'. The average of the scores is calculated by summing up all the scores and dividing by the total number of tests.

The sum of the three test scores is:
84 + 88 + x = 172 + x

And the average is:
(172 + x) / 3

To have an average between 86 and 90 inclusive, we can set up the following inequality:

86 ≤ (172 + x) / 3 ≤ 90

Let's solve this inequality step by step:

Step 1: Multiply both sides of the inequality by 3 to eliminate the fraction:
3 * 86 ≤ (172 + x) ≤ 3 * 90
258 ≤ 172 + x ≤ 270

Step 2: Subtract 172 from all parts of the inequality:
258 - 172 ≤ 172 + x - 172 ≤ 270 - 172
86 ≤ x ≤ 98

Therefore, the possible scores you can earn on your next test, 'x', to have a test average between 86 and 90 inclusive, are any scores between 86 and 98.

To determine the possible scores you can earn on your next test, we need to find the range of scores that would result in a test average between 86 and 90 inclusive.

Let's start by finding the average of your current test scores: (84 + 88) / 2 = 86.

To have an average between 86 and 90 inclusive, your next test score needs to contribute to an average of at least 86. Therefore, your total score, including the next test, should be greater than or equal to 86 multiplied by 3 (since there are now 3 test scores).

To find the minimum possible score on your next test, we subtract the sum of your current scores from the minimum average (86 * 3): (86 * 3) - (84 + 88) = 258 - 172 = 86.

So, the minimum score you can earn on your next test to have an average between 86 and 90 inclusive is 86.

Now let's find the maximum possible score on your next test. To do this, we subtract the sum of your current scores from the maximum average (90 * 3): (90 * 3) - (84 + 88) = 270 - 172 = 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, inclusive.