Tiling a floor
Carrying one area through unit conversion, wastage and cost, where each step can absorb the previous error unnoticed.
Scenario
A room measures 4.5 metres by 3.2 metres. Tiles are sold in boxes covering 1.44 square metres each, at £27 a box.
The fitter advises ordering 10 percent more than the floor area to allow for cuts and breakages, and boxes cannot be split.
Answers in order, explanations withheld, and a report on where the chain broke.
- 11.1AreaFoundation
What is the floor area?
- A14.4 square metres
- B15.4 square metres
- C7.7 square metres
- D14.04 square metres
Show the answer and reasoningHide the reasoning
14.4 square metres
Area is length times width: 4.5 x 3.2 = 14.4 square metres.
- 11.2PercentagesStandard
Builds on: The 14.4 square metres from question 1.
How much tile should be ordered once the 10 percent allowance is added?
- A15.84 square metres
- B14.4 square metres
- C15.4 square metres
- D16.4 square metres
Show the answer and reasoningHide the reasoning
15.84 square metres
Adding 10 percent multiplies by 1.10: 14.4 x 1.10 = 15.84 square metres.
- 11.3RatesChallenge
Builds on: The 15.84 square metres from question 2. Using question 1's figure instead produces one of the wrong answers here.
How many boxes are needed?
- A11
- B10
- C12
- D10.5
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11
15.84 / 1.44 = exactly 11 boxes. Working from the bare floor area instead gives 10, which would leave nothing for the cuts the allowance exists to cover.
- 11.4RatesStandard
Builds on: The eleven boxes from question 3 — and the reminder that boxes cannot be split, so the count had to be a whole number before this step.
What is the total cost of the tiles?
- A£297
- B£270
- C£324
- D£283.50
Show the answer and reasoningHide the reasoning
£297
Eleven boxes at £27 is £297. Ten boxes would be £270, which is the cost of forgetting the allowance.