SOLUTION: If a class of 6 students has an average grade of 78 before a seventh student joins, what must the seventh student get as a grade in order to raise the class average to 80?
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Question 1102635: If a class of 6 students has an average grade of 78 before a seventh student joins, what must the seventh student get as a grade in order to raise the class average to 80? Answer by greenestamps(13203) (Show Source):
The average of the 6 students is 78; the total of their scores is 78*6 = 468.
After the 7th student joins, the average of the 7 students is 80; the total of their scores is 80*7 = 560.
The score of the 7th student is the difference between the two totals: 560-468 = 92.
And here is what I think is an easier way to get to the answer to a problem like this....
3 easy calculations are required, as shown below; an explanation of each calculation is given in parentheses.
80 - 78 = 2 (The difference between the desired average and the current average is 2)
2*6 = 12 (6 students are each 2 points short of the desired average; the total number of points below the desired average is 12)
80+12 = 92 (To balance out the 12 points below average of the current 6 students, the score of the 7th student must be 12 points above the desired average)
