Question

The mean weight of 200 students in a certain class is 50 kg. The mean weight of boys in the
class is 60 kg and that of girls is 44 kg. Find the number of boys and girls in the class.
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Answer 1

Step-by-step explanation:

I'll give you two approaches to answer this question. The first approach is how I would answer this in a school assignment or examination. The second approach is how I would find the answer quickly in my mind:

First approach: 

Recalling this definition:

Mean=TotalNumber of samplesMean=TotalNumber of samples

Use this on all the numbers you see in the question and you get enough material to find the answer.

Mean weight of students (M)=Total weight of students (W)Number of students (N)Mean weight of students (M)=Total weight of students (W)Number of students (N)

Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)Mean weight of boys (Mb)=Total weight of boys (Wb)Number of boys (Nb)

Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)Mean weight of girls (Mg)=Total weight of girls (Wg)Number of girls (Ng)

So we get

60=W15060=W150

70=WbNb70=WbNb

55=WgNg=W−Wb150−Nb55=WgNg=W−Wb150−Nb

So we get three linear equations with three variables, WW, WbWb, NbNb to solve for. I'll let you complete the rest for your assignment.

Second approach: 

To quickly work it out in my mind, I would actually use a different approach. Unfortunately, my experience with using such ways in answering math questions at school has been poor. So I don't know if I can recommend this method for school assignments.

Look at the numbers closely: