Raised Garden Beds: Timber, Soil and Budget
Members of a school sustainability group plan to build three identical raised vegetable beds. Each bed is a rectangular prism with internal dimensions 2.4 m long, 1.2 m wide and 0.35 m deep. Timber is sold only in 2.4 m lengths costing $18.50 each. Each length can be cut as needed, but offcuts cannot be joined to make another side. The group will line each bed with one piece of liner costing $12.00 per bed. Soil is sold in 40 L bags at $8.90 per bag, and the supplier charges one delivery fee of $45.00 for the whole order. The group has $600.00. They decide to fill each bed to 5 cm below the top, leaving room for mulch, so the soil depth will be 0.30 m. A teacher claims the project cannot be afforded even with the reduced soil depth, but the group thinks that changing the number of beds is the only remaining option.
1. Calculate the minimum number of 2.4 m timber lengths needed for three beds and the total timber cost. Explain how the cuts work.
Read the worked answer
Each bed has perimeter 2(2.4 + 1.2) = 7.2 m.
With 2.4 m lengths, two full lengths cover 4.8 m. The remaining 2.4 m is exactly two 1.2 m sides, so one more length must be cut into two 1.2 m pieces. That gives 3 lengths per bed.
For 3 beds: 3 x 3 = 9 lengths. Timber cost = 9 x $18.50 = $166.50.
The key judgement is that the third length per bed is not wasted completely, but it cannot be used as a full side for another bed because the required side lengths are 2.4 m and 1.2 m and offcuts cannot be joined.
2. Using a soil depth of 0.30 m, calculate the soil volume, the number of 40 L bags and the total project cost. Decide whether the $600 budget is enough.
Read the worked answer
Soil volume per bed = 2.4 x 1.2 x 0.30 = 0.864 m^3. Convert to litres: 0.864 m^3 = 864 L per bed. For three beds: 3 x 864 = 2592 L.
Bags needed = 2592 / 40 = 64.8, so 65 bags if leftovers can be shared across beds. Soil cost = 65 x $8.90 = $578.50.
Total cost = timber + liner + soil + delivery = $166.50 + 3 x $12.00 + $578.50 + $45.00 = $166.50 + $36.00 + $578.50 + $45.00 = $826.00.
This is over budget by $826.00 - $600.00 = $226.00. If the group buys whole bags separately for each bed, they would need 22 bags per bed, or 66 bags, costing $587.40 and giving a total of $834.90. Either way, the teacher is correct: reducing the depth to 0.30 m is not enough for three beds.
3. Find a feasible option using two beds at the same 0.30 m soil depth. Calculate the new total cost and state one practical risk in your recommendation.
Read the worked answer
For two beds: Timber: 2 x 3 = 6 lengths, cost 6 x $18.50 = $111.00. Liner: 2 x $12.00 = $24.00. Soil volume: 2 x 864 = 1728 L. Bags: 1728 / 40 = 43.2, so 44 bags. Soil cost: 44 x $8.90 = $391.60. Delivery: $45.00 once.
Total = $111.00 + $24.00 + $391.60 + $45.00 = $571.60.
This is within the $600 budget, leaving $28.40. So building two beds is feasible, while three beds are not at this depth and size.
A practical risk is that the $28.40 buffer is small: a price rise, a cutting mistake or a need for extra soil could push the cost over $600. The group should confirm prices before ordering or reduce a dimension slightly.