A group of students are calculating their average weight. 2 other students A and B weigh 43kg and 72kg respectively.When A joins the group, their average weight becomes 61kg. After B joins the group, their average weight becomes 62kg. Determine the original average weight of the group.
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1 Answer

If n=number of students in the original group, and S=the total weight of the group, then when A joins the group, the total weight is S+43 and the number in the group is n+1; when B joins the group along with A, the total weight becomes S+43+72=S+115, and there are n+2 students altogether.

The average weight when only A has joined the group is 61=(S+43)/(n+1); and the average weight when both have joined is 62=(S+115)/(n+2). We can rewrite these equations:

61(n+1)=S+43 and 62(n+2)=S+115,

61n+61=S+43 and 62n+124=S+115,

S=61n+61-43=61n+18 and S=62n+124-115=62n+9.

Therefore S=61n+18=62n+9, and if we take the last two expressions:

62n+9=61n+18, n=9.

So S=61×9+18=62×9+9=567.

The average weight in the initial group is 567/9=63kg.

 

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