Ada's Water Errand: Unit Price Against Total Cost
Ada, a Primary Six pupil in Enugu, is sent to buy 120 sachets of water for her school's inter-house sports. Two shops sell them. Mama Ngozi's shop is at the school gate: she sells a pack of 10 sachets for ₦180, and single sachets at ₦25 each. Ada can carry the packs straight back with no fare. Oga Emeka's shop is at the market, two keke rides away; he charges ₦25 per sachet but gives one sachet free for every four bought. A keke ride costs ₦150 each way, and Ada must pay for both journeys. Ada's teacher gave her ₦2,500 and told her to bring back the change and the receipt. On the way, Ada remembers that about one sachet in twenty bursts when the packs are stacked in a basket, and the teacher will not accept a shortfall. Ada must decide quickly, because the sports start in one hour and the market trip takes 40 minutes.
1. Work out the cost of 120 sachets at each shop before fares. Show the working for the free-sachet offer clearly.
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Mama Ngozi's shop. Buying singles costs 120 × ₦25 = ₦3,000. Buying by the pack is cheaper: 120 ÷ 10 = 12 packs, and 12 × ₦180 = ₦2,160. Ada should never buy singles here; the pack price is ₦18 per sachet against ₦25.
Oga Emeka's shop. The offer is one free for every four bought, so each group of 5 sachets costs 4 × ₦25 = ₦100. Ada needs 120 sachets, and 120 ÷ 5 = 24 complete groups - it divides exactly, so no awkward remainder. She pays for 24 × 4 = 96 sachets: 96 × ₦25 = ₦2,400, and receives 24 free.
Before fares: market ₦2,400 is ₦240 more than the school gate's ₦2,160. The free-sachet offer is real but small - it works out at ₦20 per sachet, which is still above Mama Ngozi's ₦18.
2. Now include the keke fares and the ₦2,500 limit. Which shop can Ada actually use, and how much change does she return with?
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Add the fares at the market. A return trip is 2 × ₦150 = ₦300. Total at Oga Emeka's = 2,400 + 300 = ₦2,700.
Compare with the money in hand. ₦2,700 is ₦200 more than the ₦2,500 the teacher gave her. So the market trip is not merely dearer - it is impossible. Ada cannot borrow the difference, and she cannot arrive back with a shortfall and no receipt.
The school-gate option. Mama Ngozi: 12 packs = ₦2,160, no fare. Change = 2,500 − 2,160 = ₦340, and she gets a receipt immediately.
The lesson is the difference between unit price and total cost. The market's ₦20 per sachet beats the shop's ₦18? No - it does not, and even if it had, the ₦300 fare would have to be spread over the purchase before any comparison is fair. Adding transport turned a ₦240 gap into a ₦540 gap.
3. Allowing for about one sachet in twenty bursting, how many should Ada actually buy, and what is her final decision given the ₦2,500 limit and the one-hour deadline? Support your answer with numbers.
Read the worked answer
How many to buy. If 1 in 20 bursts, she keeps about 19 of every 20. To end up with 120 usable she needs 120 × 20/19 ≈ 126.3, so about 126 sachets. Since packs hold 10, she should buy 13 packs = 130 sachets, which leaves room for up to 10 burst sachets.
Cost at the school gate. 13 × ₦180 = ₦2,340. Change = 2,500 − 2,340 = ₦160. Still within budget.
Cost at the market, with the same allowance. 130 sachets means 26 groups of 5, so she pays for 104: 104 × ₦25 = ₦2,600, plus ₦300 fare = ₦2,900. Over budget by ₦400, and the 40-minute round trip leaves almost no time to spare.
Decision. Buy 13 packs from Mama Ngozi at the school gate: ₦2,340, change ₦160, a receipt in hand, and no journey. The market offer only looks attractive if you ignore the fare, the clock and the bursting.