Tiling a Room on a Fixed Budget
At a family meeting in Misrata, Salah's parents plan to tile a rectangular room measuring 4.2 m by 3.6 m. The tiles they like are square, 30 cm on each side, and are sold only in boxes of 12. Supplier A charges 18 Libyan dinars per box and gives a 10% discount on any order of 10 boxes or more; the family must collect the tiles themselves. Supplier B charges 20 dinars per box, offers no discount, but delivers free. The tiler advises adding 8% to the calculated number of tiles for cuts and breakage. Supplier A will refund only unopened full boxes; Supplier B accepts no returns. The family has budgeted 450 dinars and wants to avoid a second trip. Salah calculates 168 tiles, buys 14 boxes, and tells his father the job is covered. His older sister says the calculation is right but the decision is wrong.
1. Check Salah's tile calculation and his choice of 14 boxes. Show the arithmetic and state whether 14 boxes is sufficient.
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Room area = 4.2 × 3.6 = 15.12 m². One tile area = 0.30 × 0.30 = 0.09 m². Tiles for the bare floor = 15.12 ÷ 0.09 = 168. Salah stopped here, but the tiler's 8% allowance must be added before converting to boxes: 168 × 1.08 = 181.44, which must be rounded up to 182 tiles, because a fraction of a tile cannot be bought. Fourteen boxes contain 14 × 12 = 168 tiles - exactly the unadjusted count and 14 tiles short of the allowance. Fifteen boxes give 180 tiles, still 2 short. Sixteen boxes give 192 tiles, which covers 182 with 10 spare. So the arithmetic for the bare floor is right, but the purchasing decision is wrong: 14 boxes is not sufficient once cuts and breakage are allowed for.
2. Compare the cost at both suppliers for the correct number of boxes, taking the return policy into account, and decide which supplier the family should use.
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For 16 boxes: Supplier A's list price is 16 × 18 = 288 dinars. The order qualifies for the 10% discount because it is over 10 boxes, so the discount is 28.80 dinars and the payable amount is 259.20 dinars. Supplier B charges 16 × 20 = 320 dinars with free delivery. A is cheaper by 60.80 dinars. The return policy slightly weakens A's advantage: 16 boxes give 192 tiles, but only 182 are needed, leaving 10 tiles - not a full box - so nothing can be refunded. Even so, 259.20 dinars is well within the 450-dinar budget, and if A charged 15 dinars delivery for an order below 300 dinars, the total would be 274.20 dinars, still cheaper than B. The rational choice is Supplier A with 16 boxes, collecting the tiles to avoid a delivery charge.
3. The tiler says: 'Buy 15 boxes; the 8% is only a guess and you can always buy more.' Evaluate this advice against the family's constraints.
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The advice is unsound in this situation. Fifteen boxes contain 180 tiles, while the bare floor already needs 168 and the allowance brings the requirement to 182. Even if not a single tile breaks and every off-cut is used, 180 is still 2 tiles short. The family has also said it wants to avoid a second trip, so 'buy more later' conflicts with a stated constraint and may mean a second delivery charge or a different tile batch with a visible shade difference. The 8% figure could be too high or too low, but the direction of the risk matters: underestimating causes a shortage, whereas overestimating leaves only a few unused tiles. Since the budget allows 16 boxes, the safer decision is to buy 16, not 15.