SOLUTION: Ryan was ill and had to take the calculus test a day late. His 96 was found to raise the class average on the test from 71 to 72. How many students, including Ryan, took the test?

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Question 290213: Ryan was ill and had to take the calculus test a day late. His 96 was found to raise the class average on the test from 71 to 72. How many students, including Ryan, took the test?
(1) 22 (2) 24 (3) 26 (4) 28 (5) None of the above


Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of students who took the test efore Ryna be represented by x.
The total number of points they scored is their average * their number
PointsBeforeRyan+=+x+%2A+71
Ryan take the test and gets a 96. So let's add is score to the previous total
PointsAfterRyan+=+PointsBeforeRyan+%2B+Ryan
PointsAfterRyan+=+71x+%2B+96
You can also calculate the points after Ryan using the average method. However, there is one more student grade, so now we have x+1 students in the average
PointsAfterRyan+=+%28x%2B1%29+%2A+72
PointsAfterRyan+=+72x+%2B+72
Thus
71x+%2B+96+=+72x+%2B+72
24+=+x
So there were 24 students who took the test before Ryan took it.
Adding Ryan to that mix, we get 25 students total.
Your teacher will expect 'None of the above"
For a little fun, ask if answers 1 and 2 are both correct too :) If 25 students took the test, then certainly 21 and 22 students took it as well :) After all, you can't get 25 students to take a test if 21 and 22 didn't as well!