A 20 ft long piece of lumber is cut such that the first piece is 4 ft longer than three times each piece. What is the length of each piece?

Answer 1

F = 4 +3S

F + xS = 20 where x = the number of the other pieces, all the same length

4+3S +xS = 20

(3+x)S = 20-4 = 16

S =16/(3+x) feet for the Smaller pieces

F = 20-16/(3+x) feet for the First piece

if there's just one other piece, First piece =16 feet and the Smaller piece = 4 feet

if there's 5 other pieces, the First piece = 20-5(2)=4+3(2) = 10 feet

and the 5 Smaller pieces are each 2 feet

if there are 13 other pieces, the First piece =20-13(1) = 4+3(1)= 7 feet

and the 13 other pieces are each 1 foot

if there are 29 other pieces, the First piece = 20-29(1/2) = 4+3(1/2) = 5 1/2 feet

and the 29 other pieces are each 6 inches

if there were 61 other pieces, the First piece = 20-61(1/4)= 4+3(1/4) = 4 3/4 feet

and the other 61 pieces are each 3 inches

if there were 125 other pieces, then First piece = 20-125(1/8) = 4+3(1/8) = 4 1/8 feet

and the other 125 pieces are each 1.5 inches

there is no one solution. There are an infinite number of possible solutions

4 feet < First Piece < or = 16 feet

0 < each other piece < or = 4 feet