MathGeometry and Trigonometry4 linked questions

Tiling a floor

Carrying one area through unit conversion, wastage and cost, where each step can absorb the previous error unnoticed.

11ScenarioGeometry and Trigonometry4 linked questions

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.

  1. 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 reasoning

    14.4 square metres

    Area is length times width: 4.5 x 3.2 = 14.4 square metres.

  2. 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 reasoning

    15.84 square metres

    Adding 10 percent multiplies by 1.10: 14.4 x 1.10 = 15.84 square metres.

  3. 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
    Show the answer and reasoning

    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.

  4. 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 reasoning

    £297

    Eleven boxes at £27 is £297. Ten boxes would be £270, which is the cost of forgetting the allowance.

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