This sign shows when a lift is safe to use, Total mass of people must be 480 kg or less Fred and some other people are in the lift and their total mass is 565 kg to the nearest 5 kg. Fred, who has a mass of 88 kg to the nearest kg, gets out of the lift. Is the lift now safe to use? Yes/No You must show your working.

Concepts

Rounding, Mass, Safety Limits

Explanation

We need to determine if the lift is safe to use after Fred gets out. The total mass of people in the lift must be 480 kg or less. We are given the total mass of people in the lift (565 kg to the nearest 5 kg) and Fred’s mass (88 kg to the nearest kg). We need to calculate the possible range of the total mass and Fred’s mass, then check if the remaining mass is within the safety limit.

Step-By-Step Solution

Step 1

Determine the range of the total mass of people in the lift.

Since the total mass is 565 kg to the nearest 5 kg, the actual mass could be between:

562.5 kg and 567.5 kg

Step 2

Determine the range of Fred’s mass.

Since Fred’s mass is 88 kg to the nearest kg, the actual mass could be between:

87.5 kg and 88.5 kg

Step 3

Calculate the remaining mass in the lift after Fred gets out.

The maximum remaining mass is:

567.5 kg−87.5 kg=480 kg

The minimum remaining mass is:

562.5 kg−88.5 kg=474 kg

Step 4

Check if the remaining mass is within the safety limit.

The remaining mass ranges from 474 kg to 480 kg, which is within the safety limit of 480 kg.

Final Answer

Yes, the lift is now safe to use.