Community Garden: Fencing and Grass Seed
A community garden has a rectangular lawn 14 m long and 9 m wide. A rectangular shed 3 m by 2.5 m stands on the lawn. The garden committee wants to fence the boundary of the lawn, leaving a 1 m wide gate on one of the 14 m sides. Fence panels are 2 m wide. They can be bought singly for €18 each or in packs of four for €68. Grass seed will be spread on the lawn only, not under the shed. Each bag of seed covers 20 m² and costs €12.50. The committee must buy whole panels and whole bags. They also want to keep a spare 2 m panel in case of damage, but only if it does not push the fencing cost above €420. The treasurer has asked for the perimeter to be fenced, the number of panels and bags required, and the cheapest fencing option that meets the spare-panel condition.
1. Calculate the length of fencing needed, allowing for the gate. How many 2 m panels are required, including one spare?
Read the worked answer
Perimeter of the rectangular lawn = 2 × (14 + 9) = 2 × 23 = 46 m.
The gate is 1 m wide, so fencing length = 46 − 1 = 45 m.
Each panel is 2 m wide. Panels needed without spare = 45 ÷ 2 = 22.5.
Round up because part of a panel cannot be bought: 22.5 → 23 panels.
Add one spare panel: 23 + 1 = 24 panels.
So the committee needs 24 panels in total, including the spare.
2. Calculate the lawn area that needs seed and the number of bags required.
Read the worked answer
Area of the whole lawn = 14 × 9 = 126 m².
Area of the shed = 3 × 2.5 = 7.5 m².
Seed is not spread under the shed, so seeded area = 126 − 7.5 = 118.5 m².
Each bag covers 20 m². Number of bags = 118.5 ÷ 20 = 5.925.
Bags must be whole, so round up to 6 bags.
Check: 5 bags cover 5 × 20 = 100 m², which is not enough. 6 bags cover 120 m², which is enough and leaves 1.5 m² of coverage spare.
Cost of seed = 6 × €12.50 = €75.00.
3. Compare buying 24 panels singly with buying packs of four, and decide the cheapest option that stays within the €420 fencing budget, including the spare.
Read the worked answer
Single panels: 24 × €18 = €432. This is above the €420 budget, so it does not meet the condition.
Packs of four: each pack has 4 panels. To get 24 panels, 24 ÷ 4 = 6 packs.
Cost = 6 × €68 = €408. This is within the €420 budget.
Check a mixed option: 5 packs give 20 panels and cost 5 × €68 = €340. Four single panels cost 4 × €18 = €72. Total = €340 + €72 = €412 for 24 panels. This is also within budget but is €4 more expensive than 6 packs.
Cheapest fencing option that includes the spare panel and stays within €420 = 6 packs at €408. It provides exactly 24 panels, including one spare, and leaves €12 of the fencing budget unused.