Good at math? Help me?

Question

The average score for all students on a test was 80. The average score for thsoe who passed was 84, and the average score for those who failed was 60. If there were 60 students in the class, how many failed? please explain your reasoning so that I can understand :)

Answer 1

average = Total / Count
so

80 = Total marks of the class / 60
Total marke = 80*60 = 4800

also,
let number of failing students = x
number of passing students = 60-x

Total marks of failures / x = 60
so, total marks of failures = 60x

Total marks of passers / (60-x) = 84
so, total marks of passers = 84(60-x)

now,
Total marks of class = total failure marks + total passers marks
4800 = 60x + 84(60-x)
4800 = 5040 - 24x
24x = 5040 - 4800
24x = 240
x = 10

So 10 students failed!

Answer 2

The equation is:
80 = [84x + 60(60-x)]/60

80 is the average score for the class, which means if you add everyone's score and divide by 60, you will get 80.

84 is the average passing score, so assume all those who passed got an 84. x kids passed, so the total of those who passed is 84x.

60 is the average failing score, so assume all those who failed got a 60. (60-x) kids failed, because x is the number who passed and there are 60 kids in the class.
So the total of those who failed is 60(60-x).

80 = [84x + 60(60-x)]/60
4800 = 84x + 3600 - 60x
4800 = 24x + 3600
1200 = 24x
50 = x

x was the # passing, so 50 passed, 10 failed.

Answer 3

Let the number of students failed = x
number of students passed the exam = 60- x
Total mark obtained by 60 students = 60 * 80 =4800
Total mark obtained by the students who failed =60 x
Total mark obtained by the students who passed the exam
= (60-x) 84
60x + (60 - x) 84 = 4800
24 x = 240
x = 10
No. of students failed = 10

Answer 4

There are 60 students altogether, and they got an average score of 80, so they scored a grand total of 4,800 marks.

Let the number of students who passed be n. Thus 60 - n students fail.

Since n students pass with an average of 84, their total marks scored are 84n.
The remaining students scored a total of 60(60 - n) marks =
3,600 - 60n.

So, 84n + 3,600 - 60n = 4,800, or
24n + 3,600 = 4,800, or 24n = 1,200.

So n = 1,200/24 = 12x100/12x2 = 50.

Thus, 50 students passed.

Answer 5

suppose x student passed and y failed
therefore, x+y=60----------1
and marks scored by passed student= 84x
by failed student= 60y
total marks scored by all student= 60*80=4800

so, 84x+60y=4800
now solve 2 eqn and u will get
x=50, y=10

so no. of passed student=50 and failed=10

Answer 6

50 passed, 10 failed.

Answer 7

x=# who passed 60-x=# who failed
84x+60(60-x)=80(x+60-x)
84x+3600-60x=80(60)
24x+3600=4800
24x=1200
(24x=1200)/24
x=50

60-50=10
so 10 people failed

Answer 8

10 failed
50 passed