Tiling a Bathroom with Wastage and Cost Limits
A tiler is quoting to tile a rectangular bathroom floor measuring 2.4 m by 1.8 m and a shower recess wall measuring 1.2 m by 2.1 m. The chosen tiles are square, 300 mm on each side, sold only in boxes of 12 tiles. Tiles must be cut around the edges, and the tiler allows 10% extra for cutting and breakage on the floor and 15% on the wall because of more complex cuts. Adhesive costs $38 per 5 kg bag, and one bag covers 4 m². Grout costs $22 per 2 kg tub covering 6 m². The tiler charges labour at $65 per hour and estimates 1.5 hours per 10 m² of tiled area, rounded up to the next half hour. The customer's budget is $900.
1. Calculate the number of boxes of tiles required and the total area tiled.
Read the worked answer
Floor area = 2.4 × 1.8 = 4.32 m². With 10% wastage: 4.32 × 1.10 = 4.752 m². Wall area = 1.2 × 2.1 = 2.52 m². With 15% wastage: 2.52 × 1.15 = 2.898 m². Total area to cover = 4.752 + 2.898 = 7.65 m².
Each tile = 0.3 × 0.3 = 0.09 m². Tiles needed = 7.65 ÷ 0.09 = 85 tiles exactly. Boxes = 85 ÷ 12 = 7.08 → round up to 8 boxes (96 tiles). Note you must round up at the box level, not the tile level, or you under-order.
2. Calculate the total cost including tiles, adhesive, grout and labour, then state whether the quote meets the $900 budget.
Read the worked answer
Tiles: the question gives no tile price per box, so the cost cannot be finalised without it - a careful answer flags this. Assuming a stated price of, say, $42 per box: 8 × 42 = $336.
Adhesive: 7.65 m² ÷ 4 m² per bag = 1.91 → 2 bags × $38 = $76. Grout: 7.65 ÷ 6 = 1.28 → 2 tubs × $22 = $44. Labour: 7.65 m² ÷ 10 = 0.765, so 1.5 h per 10 m² gives 0.765 × 1.5 = 1.15 h, rounded up to the next half hour = 1.5 h. 1.5 × 65 = $97.50.
Total (with assumed tile price) = 336 + 76 + 44 + 97.50 = $553.50, within the $900 budget with $346.50 spare. The key judgement is recognising the missing tile price and rounding consumables up to whole units.
3. The customer asks to use larger 400 mm tiles instead to reduce grout lines. Explain, with calculations, how this changes the number of tiles and whether it changes the number of boxes.
Read the worked answer
Each 400 mm tile = 0.4 × 0.4 = 0.16 m². Tiles needed = 7.65 ÷ 0.16 = 47.8 → 48 tiles.
If sold in boxes of 12: 48 ÷ 12 = 4 boxes exactly. So the box count falls from 8 to 4, halving the tile order.
However, larger tiles mean the same 10%/15% wastage allowances may be too low, because edge cuts waste a larger proportion of each tile. A sound answer notes the wastage assumption should be revisited - if wastage rose to 20% overall, area = (4.32 + 2.52) × 1.20 = 8.208 m², needing 8.208 ÷ 0.16 = 51.3 → 52 tiles → 5 boxes. So the saving is real but smaller than a naive count suggests, and the judgement is that wastage percentage depends on tile size relative to the room.