Class Average

Johnny was ill and had to take a test a day late. His 96 raised the class average from 71 to 72. How many students, including Johnny, took the test?
Source: NCTM Mathematics Teacher 2006

SOLUTION
Let a_1,a_2,a_3,\cdots,a_n represent the scores of the students.
By definition of average
\dfrac{a_1+a_2+a_3+\cdots+a_n}{n}=71
Johnny’s 96 score raised the class average to 72
\dfrac{a_1+a_2+a_3+\cdots+a_n+96}{n+1}=72
a_1+a_2+a_3+\cdots+a_n+96=72(n+1)
71n+96=72n+72
n=24
Number of students including Johnny
24+1=25

Answer: 25

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About mvtrinh

Retired high school math teacher.
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