The Garden Fence: When the Minutes Are Wrong
At Government Junior Secondary School, Kwalkwalawa, the JSS3 Mathematics Club has been given ₦50,000 to fence the school garden before the rainy season. The plot is a rectangle 18 m long and 12 m wide. One of the 18 m sides already runs along the school's boundary wall, so the club agrees that no fence is needed on that side. Fence posts cost ₦450 each and must be placed at 3 m intervals, with a post at every corner. Wire mesh costs ₦1,100 per metre. A 1.5 m gate must be left open on one of the 12 m sides, and no mesh is needed across the gate. The club secretary has already written in the minutes that the work can start immediately because 'the money is enough'. The teacher asks you, as treasurer, to check the figures before any money is spent, and to bring a written recommendation to the next meeting on Friday.
1. Calculate the length of wire mesh required and the number of posts, showing every step.
Read the worked answer
Mesh. Only three sides need fencing: 18 + 12 + 12 = 42 m. The wall side is free. Take off the 1.5 m gate opening: 42 − 1.5 = 40.5 m of mesh.
Posts. The fenced part is one continuous run of 42 m, from one end of the wall to the other. Number of 3 m intervals = 42 ÷ 3 = 14, so posts = 14 + 1 = 15 posts. This already counts every corner once, because the corners fall at 0 m, 12 m, 30 m and 42 m - all multiples of 3.
Cost. Posts: 15 × ₦450 = ₦6,750. Mesh: 40.5 × ₦1,100 = ₦44,550. Total = ₦51,300.
2. Using your figures, decide whether the ₦50,000 is sufficient and write the recommendation you would present on Friday.
Read the worked answer
The total of ₦51,300 is more than ₦50,000, so the secretary's minute is wrong: the club is short by ₦1,300 before a single post is bought.
My recommendation to the meeting:
- Do not start work. Present the worked figures on one page so members can check them.
- Ask the PTA or the school for ₦2,000, not ₦1,300 - prices move, and two extra posts may be needed if the gate edges do not fall on a 3 m mark. Each extra post is ₦450 and each extra metre of mesh ₦1,100.
- If no more money is available, fence the two 12 m sides and half of the 18 m side this term and finish next term; a half-built fence is better than an unfenced garden that goats will enter.
- Correct the minutes at the next meeting so the record matches the arithmetic.
The reasoning matters more than the answer: a budget is a promise, and a treasurer who signs off on wrong figures has broken the club's trust.
3. The secretary argues that spacing posts every 4 m instead of 3 m would save money. Evaluate this argument.
Read the worked answer
The saving is small and the risk is large.
Arithmetic. 42 ÷ 4 = 10.5, so you get 10 full panels and one short 2 m panel. Worse, the side lengths (12 m and 18 m) are not multiples of 4 m, so posts cannot sit neatly at the corners and at equal spacing at the same time; in practice you still need about 12–13 posts. Saving 2–3 posts is ₦900–₦1,350 - less than the shortfall of ₦1,300 it is supposed to solve.
Practical point. The mesh costs exactly the same either way, and wide panels sag, lift at the bottom and let goats and footballs through. The fence then fails in one season and is paid for twice.
Judgement. Reject the change. Keep 3 m spacing, because 3 divides both 12 and 18, which is why the corners work out exactly.