Problema Solution
A rope 116 inches long is cut into three pieces. The middle sized piece is 10 inches shorter than twice the shortest piece. The longest piece is 5/3 as long as the shortest piece. What is the length of the shortest piece?
Answer provided by our tutors
let x, y, and z are the 3 pieces that the rope is cut into and let x<y<z
x + y + z = 116
the middle sized piece is 10 inches shorter than twice the shortest piece.
y = 2x - 10
the longest piece is 5/3 as long as the shortest piece
z = 5x/3
by solving the system of equations
x + y + z = 116
y = 2x - 10
z = 5x/3
we find
x = 27 in
click here to see the step by step solution of the system of equations
another way of solving is by plugin y = 2x - 10 and z = 5x/3 into x + y + z = 116
x + 2x - 10 + 5x/3 = 116
by solving the equation we find the same solution x = 27 in
click here to see the step by step solution of the equation
the shortest piece is 27 inches long.