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Question

Need help with this.

The average test score of a class was 65 marks. After 3 students who scored an average of 78 marks left the class, the average score of the remaining students became 62 marks. How many students were there in the class at first?

My answer is 16 students but I don’t know how to explain to DS without using algebra.

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Answer

Not sure if this counts as not algebra.

Let N be the total number of students in the class at first.

Total score at first with all students = 65N

When the 3 students left, new Total score = 65N – 3×78 = 65N – 234

If we calculate based on the new average, the new Total score = 62(N-3) = 62N – 186

Hence 65N -234 = 62N -186

3N = 48

N = 16

 

 

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post-17020

Not sure if this will be helpful ?

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Nice, graphical representation.

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Thank you for the compliment, Ender  🙂 

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These 3 students who left have each 13 points above 65. Combine they have  weighting of 13X 3= 39 points that pull up the average to 65.

Now these 39 points is lost when the 3 students leave. The effect of the 39 points loss is shared among the remaining students such that each student who was an average of 65  dropped by 3 points to 62 points.

To summarise the above statement, the 3 points dropped each is that burden they have to bear for the 39 points lost.

Number of children who bear the drop of 3 points each = 39/3 = 13 students

Originally would be 16 if you add in those three 78 pointer students.

 

Working wise is actually very simple if you DC understand the above concept, its just these few lines below,

78- 65 = 13

Total points loss = 13 X 3  =39

Number of students left  = 39/3 = 13

Originally number of students = 13 + 3 = 16 ###

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