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A carpenter used 26 ft of molding in three pieces to trim a garage door. If the long piece was 5 ft longer than twice the length of each shorter piece, what is the length of the longest piece?
\n" ); document.write( "The problem is not very well worded. Any way we assume that the shorter pieces are of the same length say S ft
\n" ); document.write( "Let the three pieces be L,S and S ft respectively.
\n" ); document.write( "The long piece is 5 ft longer than twice the length of each shorter piece
\n" ); document.write( "That is L is 5 ft longer than 2S
\n" ); document.write( "That is L = 2S +5
\n" ); document.write( " L-2S = 5 -----(1)
\n" ); document.write( "And L+S+S = 26 by data
\n" ); document.write( "That is L+2S = 26 ----(2)
\n" ); document.write( "(1) + (2) implies
\n" ); document.write( "(L-2S) +(L+2S) = 5 + 26 (adding the left with left and the right with right)
\n" ); document.write( " (L+L) = 31
\n" ); document.write( "(using additive commutativity and associativity
\n" ); document.write( "and the additive inverse law: (-2S+2S) =0)
\n" ); document.write( "Therefore 2L = 31 which means L = 31/2 = 15.5 ft
\n" ); document.write( "(2) implies L+2S = 26
\n" ); document.write( "Putting L = 15.5 in this
\n" ); document.write( "15.5 + 2S = 26
\n" ); document.write( "2S = 26.0-15.5
\n" ); document.write( "2S = 10.5 = 10.50
\n" ); document.write( "2S = 10.50
\n" ); document.write( "S = 10.50/2 = 5.25 feet
\n" ); document.write( "Therefore the three pieces are 15.5 ft, 5.25 ft and 5.25 ft and the longest piece is 15.5 ft
\n" ); document.write( "Verification:
\n" ); document.write( "15.5 + 5.25 + 5.25 = 26 which is correct.\r
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