The mean weight of 150 students in a class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. Find the number of boys and girls.

Asked by Topperlearning User | 6th Nov, 2017, 12:58: PM

Expert Answer:

begin mathsize 12px style Total space number space of space students equals 150
Let space the space number space of space boys space and space girls space be space straight x space and space straight y space respectively.
Then comma space straight x plus straight y equals 150 space space space space space.... left parenthesis 1 right parenthesis
Mean space weight space of space straight x space boys equals 70 space kg
rightwards double arrow Total space weight space of space straight x space boys equals 70 straight x space kg
Mean space weight space of space straight y space boys equals 55 space kg
rightwards double arrow Total space weight space of space straight y space boys equals 55 straight y space kg
Mean space weight space of space 150 space students equals 60 space kg
rightwards double arrow Total space weight space of space 150 space students equals 60 cross times 150 equals 9000 space kg
therefore space 70 straight x plus 55 straight y equals 9000
rightwards double arrow 14 straight x plus 11 straight y equals 1800 space space space space space.... left parenthesis 2 right parenthesis
Multiplying space equation space left parenthesis 1 right parenthesis space by space 11 comma space we space get
11 straight x plus 11 straight y equals 1650 space space space space space.... left parenthesis 3 right parenthesis
Subtracting space equation space left parenthesis 3 right parenthesis space from space left parenthesis 2 right parenthesis comma space we space have
3 straight x equals 150
rightwards double arrow straight x equals 50
Substituting space straight x equals 50 space in space left parenthesis 1 right parenthesis comma space we space get
50 plus straight y equals 150
rightwards double arrow straight y equals 150 minus 50 equals 100
Hence comma space number space of space boys equals 50 space and space number space of space girls equals 100. end style

Answered by  | 6th Nov, 2017, 02:58: PM

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