Tile Order: Area, Waste Allowance, and Whole-Box Purchasing
A homeowner is tiling a rectangular bathroom floor measuring 12 ft 6 in by 15 ft 9 in. The tiles are rectangular, 12 in by 24 in, and are sold only in boxes of 8. The installer recommends buying 10% extra to cover cuts and breakage, and any partial box must be bought whole. Unopened boxes can be returned for a full refund, but opened boxes cannot. The homeowner has budgeted for exactly 14 boxes. The installer mentions that if the homeowner chooses the diagonal layout instead of the straight layout, the waste allowance should rise to 15%.
1. Find the floor area and the area of one tile.
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Convert dimensions to decimal feet: 12 ft 6 in = 12.5 ft; 15 ft 9 in = 15.75 ft.
Floor area: 12.5 × 15.75 = 196.875 ft².
Tile area: 12 in × 24 in = 1 ft × 2 ft = 2 ft² per tile.
So the floor needs 196.875 ÷ 2 = 98.4375 tiles with zero waste - which already means at least 99 tiles, since tiles are whole units.
2. How many tiles and how many boxes are needed with the standard 10% waste allowance?
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Add waste to the area: 196.875 × 1.10 = 216.5625 ft².
Convert to tiles: 216.5625 ÷ 2 = 108.28 tiles → round up to 109 tiles. Rounding down would leave the job short, and the purpose of a waste allowance is to absorb loss, so it must not be rounded away.
Convert to boxes: 109 ÷ 8 = 13.625 boxes → round up to 14 boxes.
Fourteen boxes supply 112 tiles, leaving roughly 3 spare tiles beyond the waste allowance - the unavoidable cost of whole-box purchasing.
3. Does the 14-box budget hold if the homeowner chooses the diagonal layout? What is the practical judgement about returning boxes?
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Redo with 15% waste: 196.875 × 1.15 = 226.40625 ft² → 226.40625 ÷ 2 = 113.2 tiles → 114 tiles.
Boxes: 114 ÷ 8 = 14.25 → 15 boxes, one more than budgeted.
Judgement: the budget is $0 over only if the homeowner buys 14 boxes, which supplies 112 tiles against a 114-tile need - the job would run short with the installer already on site, and buying a single extra box later costs a second trip plus possibly a dye-lot mismatch. The reasonable move is to buy 15 boxes: the extra box is returnable unopened if the diagonal layout cuts cleaner than expected, so the downside of overbuying is limited to a temporary charge, while the downside of underbuying is a stalled job. Keep all unopened boxes sealed and labelled until the floor is finished.