A teacher announces that exams count 20% of the 1st quarter's average. If a student has a 75 average, what must he get on his exam in order to bring his grade to at least to an 82?
To find out what score the student needs on the exam in order to achieve a grade of at least 82, we can set up an equation.
Let's denote the student's exam score as "x". Since the exams count for 20% of the 1st quarter's average, this means that the remaining 80% is composed of the student's average before the exam.
Given that the student has an average of 75, we can calculate this as 80% of 75, which is 0.8 * 75 = 60.
Now, let's calculate the total grade by combining the average score before the exam with the exam score:
Total grade = (80% of average before exam) + (20% of exam score)
Total grade = 0.8 * 75 + 0.2 * x
Since we want the total grade to be at least 82, we can set up the inequality:
0.8 * 75 + 0.2 * x >= 82
To solve this inequality, we can start by subtracting 60 from both sides to isolate the term with the exam score:
0.2 * x >= 82 - 0.8 * 75
0.2 * x >= 82 - 60
0.2 * x >= 22
Finally, divide both sides of the inequality by 0.2 to solve for x:
x >= 22 / 0.2
x >= 110
Therefore, the student must get at least 110 on their exam in order to bring their grade to at least 82.