Twenty-six students in a college algebra class took a final exam on which the passing score was 70. The mean score of those who passed was 78, and the mean score of those who failed was 26. The mean of all scores was 72. How many students failed the exam?

Sinead Mcgee 2020-12-15 Answered
Twenty-six students in a college algebra class took a final exam on which the passing score was 70. The mean score of those who passed was 78, and the mean score of those who failed was 26. The mean of all scores was 72.
How many students failed the exam?
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Expert Answer

Nicole Conner
Answered 2020-12-16 Author has 97 answers
Calculation:
We need to find how many students failed in the exam.
Suppose that x students’ failed in the exam.
Therefore (26 — x) students passed in the exam.
Again, let us consider that total score of the passing students were y, and total score of the failed students were z.
Then the mean score of those who passed was 78,
y(26x)=78....(i)
The mean score of those who failed was 26,
zx=26....(ii)
The mean of all score was 72,
y+z26=72....(iii)
From the equation (iii)
y+z26=72
y=z=1872
z=1872y
Putting y=187226x in the equation (i)
y(26x)=78
187226x(26x)=78
187226x=78(26x)
187226x=202878x
78x26x=20281872
52x=156
x=3
Therefore, 3 students failed in the exam.
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