## 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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