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At a party each of 34 boys talked to 3 girls. How many girls were at the party
if each girl talked to 2 boys.
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The total number of conversation, from the boy side counting, is 34*3 = 102.
Each girl participated in 2 conversations, so, the number of girls is 102/2 = 51. ANSWER
Solved.
To make this logic more evident, let's re-formulate the problem in this equivalent form:
At a party, each of 34 boys brought 3 apples.
The apples were stored in a box.
Each girl took two apples, and the box remained empty.
How many girls were at the party ?
In this formulation, everything becomes absolutely clear and transparent,
as a well washed glass.