Answer: 99.2
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Work Shown:
Let x be the score on the next quiz. Add this x value to the other quiz scores
82.5+84+88.5+92.5+94.5+x = 442+x
note we cant combine x and 442 because we dont know the value of x yet.
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Divide this result over 6 because we want to average out 6 quiz scores
(442+x)/6
Set this result equal to the desired average we want, which is 90.2
(442+x)/6 = 90.2
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Solve for x
(442+x)/6 = 90.2
6*(442+x)/6 = 6*90.2
442+x = 541.2
442+x-442 = 541.2-442
x = 99.2
You will need a 99.2 on the next quiz so that the overall average is 90.2
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Confirming the answer:
Add up the six scores {82.5, 84, 88.5, 92.5, 94.5, 99.2} and divide by 6 to average them out
(82.5+84+88.5+92.5+94.5+99.2)/6 = 541.2/6 = 90.2
and we get the proper average we're looking for.