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 and
Step 2:
So the total rope needed
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.