Seventh Student Score

Six students in a small class took an exam. The average of their grades was 75. The seventh student in the class was ill that day and took the exam another day. When this student’s score was included, the class average rose to 78. What was the seventh student’s score?
Source: NCTM Mathematics Teacher, February 2006

SOLUTION
Imagine without loss of generality that the six students’ scores are near the average of 75, that is, some scores are below 75 and some above 75 but they don’t deviate too much from it. Let’s further assume that the six scores area as follows with the amount above or below 75 shown in parentheses
76(+1)
74(-1)
77(+2)
74(-1)
75(+0)
74(-1)
By a property of average, the amounts above and below the average sum to zero
1-1+2-1+0-1=0
When the seventh student took the exam, the average shoots up to 78. The seven students’ scores are listed again below but now compared to the new average
76(-2)
74(-4)
77(-1)
74(-4)
75(-3)
74(-4)
??(x), the seventh student score
The amounts above and below the average sum to zero
-2-4-1-4-3-4+x=0
x = 18
Score of seventh student equals 78+18=96.

Answer: 96

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About mvtrinh

Retired high school math teacher.
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