Raised Garden Design Using Three-Sided Edging
The Grade 6 outdoor learning committee has 16 m of edging to build a rectangular raised garden against the school wall. The wall forms one side, so edging is needed on only three sides. Two designs are proposed. Design A is 6 m along the wall and 5 m out from the wall. Design B is 8 m along the wall and 4 m out from the wall. The garden must have an area of at least 30 m². Soil must be 0.20 m deep. Soil is sold in 0.50 m³ bags for $8.95 each, plus 15% delivery on the soil order. The committee has $150 for soil. A student says Design A and Design B use the same amount of edging because 6 + 5 + 5 = 16 and 8 + 4 + 4 = 16, so the designs are equal. The committee needs a recommendation that considers area, cost, and the budget.
1. Compare the two designs. Does the student's statement that they are the same because both use 16 m of edging make sense? Which design should the committee choose if area is the priority?
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The student is right that both designs use 16 m of edging, but wrong that they are equal. Edging measures the three fenced sides, not the area. Design A: 6 + 5 + 5 = 16 m, area = 6 × 5 = 30 m². Design B: 8 + 4 + 4 = 16 m, area = 8 × 4 = 32 m². Both meet the minimum of 30 m², but Design B gives 2 m² more growing space for the same length of edging. If area is the priority, the committee should choose Design B. This does not yet include soil cost, so the recommendation should be checked against the $150 soil budget. The comparison also assumes the wall is straight and the garden is a true rectangle.
2. For the design you chose, calculate the number of soil bags needed and the total cost including 15% delivery. Show your rounding reasoning.
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Design B has area 8 × 4 = 32 m². Soil volume = area × depth = 32 × 0.20 = 6.4 m³. Each bag contains 0.50 m³. 6.4 ÷ 0.50 = 12.8 bags. The committee cannot buy 0.8 of a bag, and 12 bags would supply only 12 × 0.50 = 6.0 m³, which is less than 6.4 m³. So round up to 13 bags. Cost before delivery = 13 × $8.95 = $116.35. Delivery = 15% × $116.35 = $17.4525, which rounds to $17.45. Total = $116.35 + $17.45 = $133.80. The committee has $150, so Design B is affordable with $16.20 left. Rounding up is necessary because underestimating soil would leave the bed too shallow.
3. The committee wants at least 30 m² and to spend no more than $140 on soil. Does Design B meet both? Explain what recommendation you would make, using evidence from both designs.
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Design B meets both conditions. Its area is 32 m², which is at least 30 m², and its soil cost is $133.80, which is no more than $140. The margin is $140.00 − $133.80 = $6.20. Design A also meets the area minimum at 30 m², but it has less growing space. Its soil volume is 30 × 0.20 = 6.0 m³, exactly 12 bags, costing 12 × $8.95 = $107.40 plus 15% delivery ($16.11), or $123.51. Design A is cheaper but smaller. I would recommend Design B because it satisfies the area and budget constraints and provides more planting space. The committee should buy 13 bags and keep the delivery charge in the total, rather than comparing only the shelf price.