Question

Mauro has 140 ft. of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. What will the length of the longer piece be? What will the length of the shorter piece be? How do you know? Describe the process you used to solve.
Hint: There are MANY ways to solve this! If you are stuck, use your knowledge of systems of equations to solve. For example, let x be the length of the shorter piece and y be the length of the longer piece.

Answer 1

Answer:  The answer is 105 ft. and 35 ft.

Step-by-step explanation: Given that Mauro has 140 ft. of rope, which he wants to cut into two pieces such that the length of the longer piece is 3 times the length of the shorter piece.  We need to find the lengths of both the pieces.

Let 'x' and 'y' be the lengths of the longer piece and shorter piece respectively. Then, we will have the following system of equations.

$x+y=140,\\\\x=3y.$

Substituting the value of 'x' from the second equation in the first equation, we have

$x+3x=140\\\\\Rightarrow 4x=140\\\\\Rightarrow x=35.$

Thus, length of longer piece = 3 × 35 = 105 ft., and length of shorter piece = 35 ft.