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 length of the shorter piece is 35 ft, and the length of the longer piece is 105 ft.

Step by step explanation:

Let x be the length of the shorter piece. Let y be the length of the longer piece.

The first given is that the sum of the length of the shorter piece and the longer piece is 140 ft.

Therefore, x + y = 140      (1)

The second given is that  the length of the longer piece is 3 times the length of the shorter piece.

Therefore,  y = 3x       (2)

Substitute with eq (2) in eq(1):

x + 3x = 140

4x = 140

x = 35 ft

Hence, y = 3(35) = 105 ft.