Question

Three friends are cutting a length of rope to put up a tire swing. Bill needs a small piece to connect to the tire. Amy needs a piece half as long as Bill's to secure it when it's not in use. Carmen needs 5 times as much rope as Bill to climb up and connect to the branch. Write and solve an equation to find what length of rope each friend needs.

Answer 1

If 6.5x meters of rope is needed, Bill needs x meters of rope, Amy needs 0.5x meters of rope and Carmen needs 5x meters of rope.

Step-by-step explanation:

Step 1:

Assume Bill needs x meters of rope, Amy needs y meters of rope, and Carmen needs z meters of rope.

Amy needs a piece half as long as Bill's and Carmen needs 5 times as much rope as Bill.

So we have $y = 0.5x$ and $z = 5x.$

Step 2:

So the total rope needed $= x+y+z = x + 0.5x +5x = 6.5x.$

So if x = 1, x = 1 meter, y = 0.5 meters, z = 5 meters, a total of 6.5 meters of rope.

So if x = 2, x = 2 meter, y = 1 meters, z = 10 meters, a total of 13 meters of rope.