Question 1205948: To earn an A in a course, a boy must have a final average of at least 84%. On the first four examinations, he has grades of 79%, 85%, 75%, and 75%. If the final examination counts as two grades, what must he get on the final to earn an A in the course?
Found 3 solutions by josgarithmetic, math_tutor2020, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! ====
To earn an A in a course, a boy must have a  average of at least 84%. On the first four examinations, he has grades of 79%, 85%, 75%, and 75%. If the final examination counts as two grades, what must he get on the final to earn an A in the course?
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x the score for final examination;
2x representing two tests.
The first four tests and final examination count the same as 6 tests.
Solve for x.
Answer by math_tutor2020(3817) (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The correction from the second tutor is not right. The grade on the final exam counts as much as two of the other grades, so in effect 6 grades are being averaged.
Here is an alternative method for solving a problem like this involving the average of numbers that are close together.
Consider how much each of the existing grades is above or below the desired average:
79: -5
85: +1
75: -9
75: -9
Together, the four grades are -22 compared to the desired average. To achieve the desired average, the final exam must be +22 compared to the desired average.
Since the final exam counts twice as much as each of the others, the grade on the final exam must be 22/2 = 11 over the desired average.
ANSWER: The minimum grade needed to achieve an average of at least 84% is 84+11 = 95%.
CHECK: 79+85+75+75+95+95 = 504; 504/6 = 84
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