The Tiling Problem
A rectangular hall floor measures 7.2 m by 4.8 m. It is to be covered with square tiles of side 40 cm. Tiles are sold only in full boxes of 12, and each box costs $36. A 5% allowance for cutting and breakage must be added to the number of tiles needed, and the result rounded up to whole tiles before boxing. A worker calculates: area of floor = 7.2 × 4.8 = 34.56 m²; area of one tile = 0.4 × 0.4 = 0.16 m²; tiles needed = 34.56 ÷ 0.16 = 216. He then orders 216 ÷ 12 = 18 boxes exactly, with no allowance.
1. Check the worker's tile count and box order, correcting any errors.
Read the worked answer
Tile count check: 34.56 ÷ 0.16 = 216 tiles. This is correct as a raw area calculation, and it also matches a row/column check: 7.2 ÷ 0.4 = 18 tiles along the length, 4.8 ÷ 0.4 = 12 along the width, and 18 × 12 = 216. No cutting waste arises on the grid, but the 5% allowance is still required by the brief.
Allowance: 5% of 216 = 10.8, so total = 216 + 10.8 = 226.8, rounded up to 227 tiles.
Boxes: 227 ÷ 12 = 18.9..., so 19 boxes are needed.
Cost: 19 × $36 = $684.
The worker's error is twofold: he omitted the 5% allowance and he rounded the box count down to exactly 18 instead of up. Correct order: 19 boxes, $684.
2. The supplier offers a bulk deal: buy 24 boxes and get 15% off the total. Is this cheaper than the correct order, and by how much?
Read the worked answer
Correct order: 19 boxes at $36 = $684.
Bulk deal: 24 boxes at $36 = $864 before discount. 15% of 864 = 129.6, so the discounted price is 864 − 129.6 = $734.40.
Compare: $734.40 versus $684. The bulk deal is more expensive by 734.40 − 684 = $50.40.
So the bulk deal is not cheaper, despite the discount, because the buyer pays for 5 extra boxes (24 − 19) that are not needed. The discount saves $129.60 but the extra boxes cost 5 × $36 = $180, a net loss of $50.40. The correct judgement is to decline the bulk deal unless the spare tiles have another use, and to state the comparison in dollars rather than assuming a discount is always a saving.