Community Garden Fencing and Topsoil Budget
A neighborhood association is rebuilding a rectangular community garden measuring 24 meters by 18 meters. A wood-chip path 1.5 meters wide runs inside the garden along all four edges, and everything inside the path is planting bed. The outer edge will be enclosed in wire mesh costing $12.50 per meter, except for a 3-meter gate opening that needs no mesh. Topsoil is spread 5 centimeters deep over the planting beds only and is sold in bags covering 0.6 cubic meters each at $28.50 per bag. The association has raised $1,900 and will do all the labor itself. All materials are subject to 7 percent sales tax.
1. Find the area of the planting beds and the number of topsoil bags required.
Read the worked answer
Step 1 - Shrink both dimensions by the path The path runs along all four edges, so each dimension loses 1.5 m on the left and 1.5 m on the right, a total of 3 m. Length: 24 − 3 = 21 m. Width: 18 − 3 = 15 m.
Step 2 - Bed area 21 × 15 = 315 m².
Step 3 - Soil volume at 5 cm 5 cm = 0.05 m. 315 × 0.05 = 15.75 m³.
Step 4 - Bags 15.75 ÷ 0.6 = 26.25 bags → round up to 27 bags, since a partial bag cannot be bought and 26 bags supply only 15.6 m³.
A common slip is subtracting 1.5 m from each dimension instead of 3 m; that error inflates the bed to 22.5 × 16.5 = 371.25 m² and overstates the soil by roughly 2.8 m³.
2. What do the fencing and topsoil cost together, including tax, and does the project fit the $1,900 budget?
Read the worked answer
Fencing length Perimeter = 2(24 + 18) = 84 m. Less the 3 m gate: 84 − 3 = 81 m of mesh. 81 × $12.50 = $1,012.50.
Topsoil 27 bags × $28.50 = $769.50.
Materials subtotal 1,012.50 + 769.50 = $1,782.00.
Tax at 7% 1,782.00 × 0.07 = $124.74.
Total 1,782.00 + 124.74 = $1,906.74.
Verdict: Over budget by $6.74. The gap is small but real - the association cannot simply round the total down, because the bag count is already at the minimum whole number and the tax is not negotiable.
3. One member proposes spreading the topsoil only 4.5 cm deep instead of 5 cm. Does that bring the project within budget? Show the arithmetic and state the trade-off.
Read the worked answer
Step 1 - New volume 315 × 0.045 = 14.175 m³.
Step 2 - New bag count 14.175 ÷ 0.6 = 23.625 → 24 bags. 24 × $28.50 = $684.00.
Step 3 - New subtotal 1,012.50 + 684.00 = $1,696.50.
Step 4 - Tax 1,696.50 × 0.07 = $118.76 (118.755).
Step 5 - Total 1,696.50 + 118.76 = $1,815.26.
Verdict: Yes - $84.74 under the $1,900 cap, with room to absorb a price change.
Trade-off: A shallower bed dries out faster, gives roots less depth, and will need topping up sooner. The savings come from dropping three bags, so the member should confirm that 4.5 cm still meets the plants the association intends to grow before committing.