Problema Solution
A 56-inch board is cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.
Answer provided by our tutors
let
x = the length of the first piece
y = the length of the second piece
z = the length of the third piece
56-inch board is cut into three pieces
x + y + z = 56
the second piece is 3 times as long as the first piece
y = 3x
the third piece is 4 times as long as the first piece
z = 4x
by solving the system of equations
x + y + z = 56
y = 3x
z = 4x
we find
x = 7 in
y = 21 in
z = 28 in
the lengths of the 3 pieces are 7, 21 and 28 inches.