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In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class?
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In a class with a certain number of student if a teacher weighing 76 k...
Problem:
In a class with a certain number of students, if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg. If one more teacher weighing 50 kg is added. Then the average weight of the class increases by 3 kg over the original average. What is the original average weight (in kg) of the class? Explain in detail.
Solution:
Let us assume that there are 'n' number of students in the class and the original average weight of the class is 'x' kg.
Therefore, the total weight of all the students in the class = nx
When the teacher weighing 76 kg is added, the new total weight of the class becomes:
nx + 76
The new average weight of the class = (nx + 76)/(n + 1) kg
It is given that the new average weight of the class is increased by 2 kg. Therefore,
(nx + 76)/(n + 1) = x + 2
On solving the above equation, we get:
nx + 76 = xn + x + 2n + 2
nx - xn + 76 - x - 2n - 2 = 0
-x(n-1) - 2(n-1) + 74 = 0
-x(n-1) - 2(n-1) = -74
x(n-1) + 2(n-1) = 74
x(n-1) = 74 - 2(n-1)
x(n-1) = 76 - 2n
Now, when one more teacher weighing 50 kg is added, the total weight of the class becomes:
(nx + 76) + 50 = nx + 126
The new average weight of the class = (nx + 126)/(n + 2) kg
It is given that the new average weight of the class increases by 3 kg over the original average. Therefore,
(nx + 126)/(n + 2) = x + 3
On solving the above equation, we get:
nx + 126 = xn + 3n + 2x + 6
nx - xn + 126 - 3n - 2x - 6 = 0
-x(n-1) - 3(n-1) + 120 = 0
-x(n-1) - 3(n-1) = -120
x(n-1) + 3(n-1) = 120
Substitute the value of (n-1) from the previous equation we derived:
76 - 2n + 3(n-1) = 120
76 - 2n + 3n - 3 =
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In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class?
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In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class?.
In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class with a certain number of student if a teacher weighing 76 kg is added then average weight of class is increased by 2 kg.if one more teacher weighing 50 kg is added. then the average weight of the class increases by 3 kg over the original average. what is the original average weight (in kg) of the class?.
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