Calculating with upper and lower bounds - Higher

In these calculations we need to think about:

• whether we need upper or lower bounds
• whether to add, subtract, multiply or divide
• how sensible our answers are

Question

A sack of sand weighs 20 kg measured to the nearest kg. It is used to fill bags that will contain 250 g of sand measured to the nearest 10 g. Work out the maximum number of bags that can be filled.

Solution

To find the maximum number of bags that can be filled, we need the maximum possible total weight of the sack and the minimum possible weight in each bag. Then we need to divide the maximum sack weight by the minimum bag weight.

The maximum weight for the sack is 20.5 kg.

The minimum weight for each bag is 245 g.

Before we can divide, the units need to be the same. Convert kilograms into grams by multiplying by 1000.

20.5 kg = 20,500 g

20500 ÷ 245 = 83.67…

Normally we would round 83.67… to 84, but in this case it is not practical as the last bag did not fill completely. Therefore the maximum number of bags that could be filled is 83.

Question

A hoist can lift 1,600 kg, given to 2 significant figures. It is being used to load boxes that weigh 48 kg to the nearest kg.

How many boxes can the hoist safely lift?

Solution

For a quick recap on significant figures see the section Significant figures.

For safety we need to think about the lower limit for the hoist and the higher limit for each box.

The lower limit for the hoist is 1,550 kg.

The higher limit for each box is 48.5 kg.

1550 ÷ 48.5 = 31.9….

Even though this is very close to 32, the hoist can only lift 31 boxes safely.