Question

Ross wants to cut a 40-foot rope into two pieces so that the length of the first piece divided by the length of the second piece is 2.

a. Let x represent the length of the first piece. Write an equation that represents the relationship between the pieces as stated above.

b. What values of x are not permissible in this equation? Describe within the context of the problem what situation is occurring if x were to equal this value(s). Rewrite as a system of equations to exclude the value(s).

c. Solve the equation to obtain the lengths of the two pieces of rope. (Round to the nearest tenth if necessary.)

Answer 1

Answer and Step-by-step explanation:

40-foot

two pieces = length of the first piece divided by the length of the second piece is 2.

a. first piece: x

second piece: y

x/y = 2 ∴ x = 2y

b. y = 0 ∴ x = 0

If he divides the rope, we have x and y ≠ 0.

c. x+y = 40

x = 2y

2y + y = 40

3y = 40

y = 40/3

y = 13.3