The total number of eggs the family had is 3 * 12 = <<3*12=36>>36 eggs
If each adult received 3 eggs, the total number of eggs they got is 3 * 3 = <<3*3=9>>9 eggs.
The children shared 36 - 9 = <<36-9=27>>27 eggs
Since each girl received an egg, the boys shared 27 - 7 = <<27-7=20>>20 eggs
If each boy received 1 egg more than each girl, each received 1+1 = <<1+1=2>>2 eggs
The boys received 20 eggs, and if each got 2 eggs, then 20/2 = <<20/2=10>>10 boys went on the trip
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