SOLUTION: Johnny was ill and had to take a test a day late. His 99 raised the class average from 71 to 75. How many students, including Johnny, took the test?

Question 620819: Johnny was ill and had to take a test a day late. His 99 raised the class average from 71 to 75. How many students, including Johnny, took the test?

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Johnny was ill and had to take a test a day late. His 99 raised the class average from 71 to 75. How many students, including Johnny, took the test?
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The average score is determined by:
average = S/n, where S = the sum of scores and n is the number of students
Let S = the sum of scores before Johnny took the test
Let n = the total number who took the test
Then the original class average = 71 = S/(n-1)
The adjusted average with Johnny's score included = 75 = (S+99)/n
We have two equations and two unknowns
Cross-multiplying gives
71(n-1) = S [1]
75n = S + 99 [2]
Subtract [1] from [2]:
4n + 71 = 99
4n = 28
n = 7
So 7 students took the test

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