text: The most important thing in any word problem is figuring out how to set it up.  Our intrepid builder cut a total of 6 boards, and used the longer pieces from all of them, so he used 6x feet of wood.  Additionally, he used 4 of the smaller pieces, each of which is (16 - x) feet long.  This accounts for another 4(16 - x) feet.  This all has to add up to 82 feet of boards, so we get the equation:\n\n6x + 4(16 - x) = 82\n\nThis simplifies as follows:\n\n6x + 64 - 4x = 82\n2x + 64= 82\n\nThe final answer is left as an exercise for the reader.