Question

A length of rope is 144 cm. The scout leader the rope into 3 pieces. One piece is twice as lo as the shortest piece. The other piece is three times as long as the shortest piece. What is the length of each piece of rope?​

Answer 1

Answer: a = 24 cm, b = 48 cm, c = 72 cm

Step-by-step explanation: use a, b, and c to represent each piece of rope. Assuming that a is the shortest piece, we can use the following equations to represent the problem:

length of a = a

length of b = 2a

length of c = 3a

length of whole rope = a + b + c = 144 cm

plug in our variables into the equation to find the length of a, the shortest piece:

(a) + (2a) + (3a) = 144 cm

6a = 144 cm (combine like terms)

a = 24 cm (divide both sides by 6 to isolate a)

plug a = 24 cm into our earlier equations:

a = 24 cm

b = 2(24 cm) = 48 cm

c = 3(24 cm) = 72 cm

Yay, you're done!