Paper order before the mock examinations
Kabelo runs the printing kiosk at a secondary school and must order 46 reams of A4 paper before the mock examinations. The school store has one shelf with a clear height of 2.5 m, and every ream is 5.2 cm thick. Supplier A sells paper only in sealed packs of 5 reams at P172.50 per pack and delivers free of charge. Supplier B sells any number of single reams at P36.00 each and charges a flat P25.00 delivery fee per order, whatever the size of the order. The kiosk has P1 750 available for paper, and Kabelo does not want more than a few spare reams left over when the examinations end.
1. Which supplier should Kabelo use? Support your answer with calculations covering the cost, the number of spare reams and the storage limit.
Read the worked answer
Supplier A (packs of 5 only)
46 ÷ 5 = 9.2, so he must buy 10 packs.
- Reams delivered: 10 × 5 = 50, so 4 reams are spare.
- Cost: 10 × P172.50 = P1 725.00 (inside the P1 750 budget).
- Shelf height needed: 50 × 5.2 cm = 260 cm = 2.6 m, which is more than 2.5 m, so the paper will not fit on the shelf.
Supplier B (single reams plus delivery)
- Cost: 46 × P36.00 = P1 656.00, plus P25.00 delivery = P1 681.00 (inside the budget).
- Reams delivered: exactly 46, so 0 spare.
- Shelf height needed: 46 × 5.2 cm = 239.2 cm ≈ 2.39 m, which fits under 2.5 m.
Decision: use Supplier B. It is P1 725.00 − P1 681.00 = P44.00 cheaper, leaves no surplus paper, and is the only option that fits the shelf. The lower price per ream from Supplier A (P172.50 ÷ 5 = P34.50) is misleading because the pack size forces him to buy 50 reams, not 46.
2. The deputy principal suggests ordering 50 reams so that nothing runs short. Using the same two suppliers, what would 50 reams cost from each, and does the answer to the first task change?
Read the worked answer
Supplier A: 50 ÷ 5 = 10 packs exactly, so 10 × P172.50 = P1 725.00, with no spare reams.
Supplier B: 50 × P36.00 = P1 800.00, plus P25.00 delivery = P1 825.00.
At 50 reams Supplier A is cheaper by P1 825.00 − P1 725.00 = P100.00, and it also stays inside the P1 750 budget while Supplier B would be P75.00 over it.
However, the storage problem does not disappear: 50 reams still need 2.6 m of shelf height against the 2.5 m available. So the advice only changes if the extra 4 reams can be stored somewhere else (for example a locked cupboard). If the shelf is the only store, Supplier B remains the practical choice; if extra storage can be found, Supplier A becomes the better buy at 50 reams.
3. A ream contains 500 sheets. Write the thickness of a single sheet in metres, giving your answer in standard form.
Read the worked answer
A ream is 5.2 cm thick, so one sheet is
5.2 cm ÷ 500 = 0.0104 cm.
Convert to metres: 0.0104 cm ÷ 100 = 0.000104 m.
In standard form, move the decimal point 4 places to the right, so the number lies between 1 and 10:
0.000104 = 1.04 × 10⁻⁴ m.
Check: 1.04 × 10⁻⁴ × 500 = 0.052 m = 5.2 cm, which matches the thickness of one ream.