3.3.1 Try some yourself
A friend has been quoted a price of £25.50 per square yard for tarmac surfacing of his yard. The yard measures 6 yards by 10 feet. Here is his calculation of the total cost. What is wrong with it?
cost = £25.50 × 6 × 10 = £1530
He has not used the same units. The figure 10 he used refers to feet, so in a calculation using yards he needs 10/3 (3 feet = 1 yard). The cost should be
Another friend, Kim, wishes to reproof her tent. A litre tin of ‘proofing agent’ states that the coverage is roughly 5 square metres per litre. The manufacturer's measurements of the tent, which is a ridge tent, are: height 2 m, length 3 m. However, Kim realises that she needs the other measurements. Here is her diagram and calculation.
The problem: how many litres of proofing agent to buy to cover the tent?
Area of 2 side panels 2 × 3 × 250 = 1500
Area of end door panels together 2 × 150 + 150 = 450
Total area = 1950
Number of litres = 1950 ÷ 5 = 390
Kim thinks this is rather a lot and asks you to help. Find her errors.
The errors are
Not converting the centimetres to metres.
The order of operations for calculating the end door panels.
Correct answer should be
sides 2 × 3 × 2.5 = 15 metres squared
doors 2 × (1.5 + 1.5) = 6 metres squared
Total area = 21 metres squared
Number of litres = 21 ÷ 5 = 4.2 litres
Therefore Kim needs to buy 5 litres of proofing agent.