Question

A 10-ft. board is cut into 2 pieces so that one piece is 6 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. 1st Piece 2nd Piece 3rd Piece:

Answer 1

x = length of shorter piece

3x+6 = length of longer piece

The two pieces add to 10 ft, assuming negligible or a very small amount of scrap waste.

smaller + larger = 10

(x) + (3x+6) = 10

4x+6 = 10

4x = 10-6

4x = 4

x = 4/4

x = 1

The smaller piece is 1 ft long.

3x+6 = 3*1+6 = 9

The larger piece is 9 ft long. Or we could say 10-1 = 9 since the two pieces add up to 10 feet.

Answers:

smaller piece = 1 ft

larger piece = 9 ft