Math Problem 1
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A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
Re: Math Problem 1
Here is my solution:
The average mark of the students is $70$
the total obtained marks will be $70*2=140$, since
AVERAGE = SUM OF THE QUANTITY$/$NUMBER OF QUANTITIES
NOW, given that the number of student is $20$,
we can take that,
number of students scoring $ < 60 = 10$
number of students scoring $ > 60 = 10$
But,
calculating the sum we get that the result is $1250 [(10*50)+(10*75)]$, we have a shortfall of $150.$
so we have to divide $150$ by $25$ since adding a student in the group where the the average is $75$, results in adding $25$ to the result.
BUT WHY??
Because taking value as $0$ where the group where the average is sixty , we get that :
$1$. emitting a student from that group results in the total number going down by $25$
$2$. adding a student in the group where the average is $75$ results in adding $25$ to the total marks since
$75-50=25$
After division we get that:
$150/25=6$
therefore, number of students who got below $60$ is $(10-6)=4$ (answer)
Note:If you have any questions or problems regarding this or any other better solutions, please do post it quickly
The average mark of the students is $70$
the total obtained marks will be $70*2=140$, since
AVERAGE = SUM OF THE QUANTITY$/$NUMBER OF QUANTITIES
NOW, given that the number of student is $20$,
we can take that,
number of students scoring $ < 60 = 10$
number of students scoring $ > 60 = 10$
But,
calculating the sum we get that the result is $1250 [(10*50)+(10*75)]$, we have a shortfall of $150.$
so we have to divide $150$ by $25$ since adding a student in the group where the the average is $75$, results in adding $25$ to the result.
BUT WHY??
Because taking value as $0$ where the group where the average is sixty , we get that :
$1$. emitting a student from that group results in the total number going down by $25$
$2$. adding a student in the group where the average is $75$ results in adding $25$ to the total marks since
$75-50=25$
After division we get that:
$150/25=6$
therefore, number of students who got below $60$ is $(10-6)=4$ (answer)
Note:If you have any questions or problems regarding this or any other better solutions, please do post it quickly
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Re: Math Problem 1
Your heuristic approach of solving the problem is commendable.
How about this approach: you assume the no. of students who scored less than 60 to be 'x' and then construct a simple algebraic equation?
How about this approach: you assume the no. of students who scored less than 60 to be 'x' and then construct a simple algebraic equation?