Tiles, Wastage and a Brother-in-Law's Advice
Mrs Okoro is tiling the floor of a rectangular room 3.6 m long and 4.2 m wide. She chooses square tiles measuring 30 cm by 30 cm, sold only in boxes of 12. Each box costs ₦9,600. The tiler advises her to allow 5% extra tiles for cutting along the walls and for breakages, and he charges ₦1,500 per square metre of floor laid. Mrs Okoro's brother-in-law, a builder, tells her to buy 14 boxes because 'the room is about 15 square metres and each box covers about 1.1 square metres, so 14 boxes is plenty.' Mrs Okoro also needs a bag of cement for grout at ₦7,500, and she must pay the tiler for the full floor area even though off-cuts are wasted. She has saved ₦180,000 and wants to know, before she pays, whether the money will finish the job and whether her brother-in-law's figure will leave her short.
1. Calculate the floor area, the exact number of tiles required, the number needed after the 5% allowance, and hence the number of boxes to buy. Show what 14 boxes actually covers.
Read the worked answer
Floor area: 3.6 × 4.2 = 15.12 m² (the brother-in-law's 'about 15' is already slightly low).
One tile: 30 cm × 30 cm = 0.3 × 0.3 = 0.09 m².
Exact tiles: 15.12 ÷ 0.09 = 168 tiles.
With 5% allowance: 168 × 0.05 = 8.4, so 168 + 8.4 = 176.4 tiles. Tiles are whole objects and you cannot buy part of one, so round up: 177 tiles.
Boxes: 177 ÷ 12 = 14.75 boxes, and boxes are sold whole, so 15 boxes = 180 tiles.
What 14 boxes gives: 14 × 12 = 168 tiles = 15.12 m² exactly. That is the bare floor with not one spare tile. The 5% allowance exists precisely because tiles must be cut at the walls and some break; with 168 tiles there is zero margin, so the job stops the moment one tile cracks or one cut is mis-measured. The brother-in-law rounded down a number that had to be rounded up.
2. Calculate the total cost of the job - tiles, tiler's charge and cement - and state whether Mrs Okoro's ₦180,000 is enough, with the change.
Read the worked answer
Tiles: 15 boxes × ₦9,600 = ₦144,000.
Tiler: he charges for the floor area laid, not for tiles bought: 15.12 × ₦1,500 = ₦22,680.
Cement: ₦7,500.
Total: 144,000 + 22,680 + 7,500 = ₦174,180.
Change from ₦180,000: 180,000 − 174,180 = ₦5,820.
The money does finish the job, but only just - about 3% of the budget is left. That margin matters: if the tiler finds the floor uneven and needs a second bag of cement, or if more than 12 tiles are lost to breakages, the ₦5,820 disappears quickly. Note also that if she had bought the 14 boxes her brother-in-law suggested, she would save ₦9,600 but risk running out of tiles partway through, and a later matching box may cost more or be from a different shade batch.
3. State the rounding rule this problem teaches, and explain what would go wrong if a pupil rounded the tile count down before adding the wastage.
Read the worked answer
The rule. In a buying problem, every intermediate quantity that must be a whole object is rounded up, never down, and the wastage is added before the final rounding, not after.
What goes wrong if you round first. A pupil who rounds 176.4 down to 176 and then divides by 12 gets 14.67 → 15 boxes, which happens to give the right answer here. But a pupil who rounds 168 ÷ 12 = 14 boxes first, then adds 5% as '14 plus a bit of a box', concludes that 14 boxes will do. That is exactly the brother-in-law's error: the 5% allowance has been applied to a number that has already lost its fractional part, so the spare tiles have effectively been rounded away.
The general habit to build: compute the exact requirement, add the allowance as a percentage of that exact figure, round up to whole tiles, then round up again to whole boxes. Rounding down at any stage means buying less than the job needs, and the failure only appears on the last day of work, when it is expensive to fix.