Need help in solving this
To receive an A grade, a student must average 100 or less but more than 93. If Zane received an A in the course and had five grades of 95, 92, 98, 76, and 100 before taking the final exam, what were the possible grades for his final if there were 100 points possible? (Assume all six grades are weighted equally and let x represent the unknown score.)
mean = ∑x/n
93 = (95+92+98+76+100+x)/6
Solve for x. x ≥ ?
To find the possible grades for Zane's final exam in order to receive an A grade, we can use the given information.
Let's start by calculating Zane's current average before the final exam. We sum up all his previous grades and divide by the total number of grades:
(95 + 92 + 98 + 76 + 100) / 5 = 461 / 5 ≈ 92.2
Zane's current average is approximately 92.2.
To receive an A grade, Zane's average must be 100 or less but more than 93. Therefore, we need to find the possible values of the final grade (x) that will result in an average within this range.
Let's set up an inequality to represent the conditions:
93 < (461 + x) / 6 ≤ 100
Now we can solve this inequality to find the range of possible values for the final grade.
1. Multiply both sides of the inequality by 6 to eliminate the fraction:
6 * 93 < 461 + x ≤ 6 * 100
2. Simplify:
558 < 461 + x ≤ 600
3. Subtract 461 from all sides:
558 - 461 < 461 + x - 461 ≤ 600 - 461
97 < x ≤ 139
Therefore, the possible grades for Zane's final exam range between 97 and 139 (inclusive) in order to receive an A grade.
Please note that this is based on the assumption that all six grades are weighted equally.