Your test scores in one class are 78 and 86. What possible scores can you earn on your next test to have a test average between 82 and 88, inclusive?
To find the possible scores on the next test, we can calculate the minimum and maximum average by adding the current test scores and the possible score on the next test and dividing by 3.
Minimum average: (78 + 86 + x) / 3 = 82
Simplifying the equation: 164 + x = 246
Solving for x: x = 82
Maximum average: (78 + 86 + x) / 3 = 88
Simplifying the equation: 164 + x = 264
Solving for x: x = 100
Therefore, the possible scores on the next test to have a test average between 82 and 88, inclusive, are 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, and 100.
To determine the range of possible scores on the next test to have a test average between 82 and 88 (inclusive), we need to consider the current test scores and the average formula:
Average = (sum of all test scores) / (number of tests)
Let's use the variable 'x' to represent the score on the next test.
Given test scores: 78, 86
Average range: 82 to 88
We can set up the following inequality:
(78 + 86 + x) / 3 ≥ 82
First, let's solve the inequality for the lower bound:
(78 + 86 + x) / 3 ≥ 82
164 + x ≥ 246
x ≥ 246 - 164
x ≥ 82
Next, let's set up the inequality for the upper bound:
(78 + 86 + x) / 3 ≤ 88
164 + x ≤ 264
x ≤ 264 - 164
x ≤ 100
Therefore, the possible scores on the next test to have a test average between 82 and 88 (inclusive) are x ≥ 82 and x ≤ 100.
To find the possible scores you can earn on your next test, we can use the average formula. The formula for finding the average is:
Average = Sum of all numbers / Total number of numbers
In this case, we have two test scores, 78 and 86. Let's call the score on the next test "x". We want the average of all three tests to be between 82 and 88 inclusive.
So, we can set up an inequality to represent this:
82 ≤ (78 + 86 + x) / 3 ≤ 88
To solve this inequality, we can multiply both sides by 3 to eliminate the denominator:
246 ≤ 78 + 86 + x ≤ 264
Next, we can combine like terms:
246 + (-78 - 86) ≤ x ≤ 264 + (-78 - 86)
Which simplifies to:
82 ≤ x ≤ 100
Therefore, the possible scores you can earn on your next test to have an average between 82 and 88 inclusive are any score between 82 and 100.