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Elmer has taken n tests.  If he receives 73  on the next test, his average will be exactly 83.  If he receives 99, then the average will be exactly 87.  What does n equal?

 May 9, 2020
 #1
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It seems to work for n = 5 tests before the last. But the average of 87 comes out as 87 1/3 !! Did you make a mistake somewhere in the question?

 May 9, 2020
 #3
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(a * n + 73)/(n + 1)=83, 

(a * n + 97)/(n +1) =87, solve for a, n

Note: I adjusted the last score of 99 to 97. And now you get:

n =5 tests before the last

a =85 - average score before the last test.

Guest May 9, 2020
 #2
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"Elmer has taken n tests.  If he receives 73  on the next test, his average will be exactly 83.  If he receives 99, then the average will be exactly 87.  What does n equal?"

 

(x + 73)/(n + 1) = 83   ...(1)

 

(x + 99)/(n + 1) = 87   ...(2)

 

Rewrite (1) as x + 73 = 83*(n + 1)   ...(3)

and (2) as       x + 99 = 87*(n + 1)   ...(4)

 

Subtract (3) from (4):  26 = 4n + 4  so  n = 5.5    Elmer took 5.5 tests??????

 May 9, 2020
edited by Alan  May 9, 2020
edited by Alan  May 9, 2020

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