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.
To find the possible scores on the next test, we need to determine the overall score range for the class average.
The current average is given by (81 + 85 + x) / 3, where x represents the score on the next test.
To find the range, we multiply the current average (83) by 3, and the current average (88) by 3.
Hence, the overall score range is 249 to 264.
Setting up an inequality:
249 ≤ (81 + 85 + x) / 3 ≤ 264
Multiplying through by 3:
747 ≤ 81 + 85 + x ≤ 792
Combining like terms:
747 ≤ 166 + x ≤ 792
Subtracting 166 from all parts of the inequality:
581 ≤ x ≤ 626
Therefore, the possible scores on the next test to have a test average between 83 and 88 inclusive range from 581 to 626.
To find the possible scores you can earn on your next test, we need to compute the average of the three scores.
Let "x" be the score you earn on your next test.
The average of the three scores is given by:
(81 + 85 + x) / 3
To have a test average between 83 and 88 inclusive, we can set up the following inequality:
83 ≤ (81 + 85 + x) / 3 ≤ 88
To solve this inequality, we can multiply each part of the inequality by 3:
3 * 83 ≤ 81 + 85 + x ≤ 3 * 88
Simplifying the inequality, we get:
249 ≤ 166 + x ≤ 264
Subtracting 166 from each part of the inequality, we get:
249 - 166 ≤ x ≤ 264 - 166
Simplifying, we have:
83 ≤ x ≤ 98
Therefore, the possible scores you can earn on your next test to have a test average between 83 and 88 inclusive are any scores between 83 and 98.
To find the possible scores you can earn on your next test, you need to determine the range of values that will give you an average between 83 and 88 inclusive.
First, let's determine the minimum average score possible. We'll assume the next test score is the lowest possible value. To calculate the minimum average, we will add this test score to the sum of your current scores and divide by the total number of tests (3 in this case since you have two previous scores and one upcoming test).
Minimum average = (81 + 85 + x) / 3
Next, let's determine the maximum average score possible. We'll assume the next test score is the highest possible value. To calculate the maximum average, we will add this test score to the sum of your current scores and divide by the total number of tests (3 in this case).
Maximum average = (81 + 85 + x) / 3
Now, we know that the average score should be between 83 and 88 inclusive. So we have the following inequality:
83 ≤ (81 + 85 + x) / 3 ≤ 88
To solve the inequality, we'll first multiply everything by 3 to get rid of the fraction:
3 * 83 ≤ (81 + 85 + x) ≤ 3 * 88
249 ≤ (166 + x) ≤ 264
Next, we'll simplify the inequality:
249 - 166 ≤ x ≤ 264 - 166
83 ≤ 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 between 83 and 98 inclusive.