SOLUTION: In Professor Tuffguy's mathematics class, 36 students took the final exam. Of the average passing grade was 78, the average failing grade was 60, and the class average was 71, how

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Question 449517: In Professor Tuffguy's mathematics class, 36 students took the final exam. Of the average passing grade was 78, the average failing grade was 60, and the class average was 71, how many of these 36 students passed the final?
A) 14
B) 22
C) 24
D) 29
Please explain your reasoning. Thank you.
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In Professor Tuffguy's mathematics class, 36 students took the final exam.
Of the average passing grade was 78, the average failing grade was 60, and the class average was 71,
how many of these 36 students passed the final?
:
Let x = number of students that passed
then
(36-x) number of students who failed
:
The average equation
:
passed + failed, divided by 36 = 71
%2878x+%2B+60%2836-x%29%29%2F36 = 71
multiply both sides by 36
78x + 60(36-x) = 36(71)
78x + 2160 - 60x = 2556
78x - 60x = 2556 - 2160
18x = 396
x = 396%2F18
x = 22 students passed

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula
average = (sum of data)/(number of data items)
and
sum of data = (average)*(number of data items)
Let n = number of students who passed
Let k = sum of passing grades
+2556+-+k+ = sum of failing grades
------------------------------------
The class average was 71 and there are 36 students
sum of grades = 71%2A36+=+2556
----------------------------
The students either passed or failed, so
passing + failing = 36
passing = +n+
failing = +36+-+n+
----------------
average of passing students = 78
(1) +78+=+k%2Fn+
average of failing students = 60
(2) +60+=++%282556+-+k%29+%2F+%2836+-+n%29+
---------------------------
This is 2 equations and 2 unknowns, so it's solvable
(1) +78+=+k%2Fn+
(1) +k+=+78n+
Substitute this in (2)
(2) +60+=++%282556+-+78n%29+%2F+%2836+-+n%29+
(2) +60%2A%2836+-+n%29+=+2556+-+78n+
(2) +2160+-+60n+=+2556+-+78n+
(2) +18n+=+396+
+n+=+22+
22 students passed the final
check:
(1) +k+=+78n+
(1) +k+=+78%2A22+
(1) +k+=+1716+
(2) +60+=++%282556+-+k%29+%2F+%2836+-+n%29+
(2) +60+=++%282556+-+1716%29+%2F+%2836+-+22%29+
(2) +60+=+840%2F14+
++60+=+60+
OK