2/3 < k/27 < 8/9
9/9 • 2/3 < k/27 < 3/3 • 8/9
18/27 < k/27 < 24/27
18 < k < 24
If k is an integer, then it can be any of {19, 20, 21, 22, 23}. The sum of these integers is 105.
Question: What is the sum of the positive integers k such that k/27 is greater than 2/3 and less than 8/9?
The sum of the positive integers k such that k/27 is greater than 2/3 and less than 8/9 is 105.
Linear Inequations are relations between two or more expressions showing the relationship between these expressions with any of the operators: greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤).
The question is a basic linear inequality question, where we are told that k is a positive integer such that k/27 is greater than 2/3 and less than 8/9.
We are asked to find the sum of all possible values of k.
Writing the given linear inequation, we get
2/3 < k/27 < 8/9.
To solve, we multiply each term by 27,
(2/3)*27 < (k/27)*27 < (8/9)*27
or, 18 < k < 24.
So, now we can see that k is greater than 18 and less than 24. We are also told that k is a positive integer, so we can write these values of k satisfying the above inequation:
k = {19, 20, 21, 22, 23}
Now we calculate sum of all possible values of k,
Sum = 19 + 20 + 21 + 22 + 23 = 105.
∴ The sum of the positive integers k such that k/27 is greater than 2/3 and less than 8/9 is 105.
Learn more about Linear Inequalities at
https://brainly.com/question/19383157
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