The School Garden Water Budget
A school garden has a rectangular plot 12 meters long and 8 meters wide, plus a triangular herb bed with a base of 6 meters and a height of 4 meters. The garden club must cover the rectangular plot with mulch at a depth of 5 centimeters. Mulch is sold in bags of 0.05 cubic meters each, and each bag covers 1 square meter at the required depth. The club has a budget of $90, and bags cost $7 each. A teacher says, 'Just buy 12 bags-one per meter of length-and you'll be fine.' The triangular bed will not be mulched this year.
1. Compute the area of the rectangular plot and the number of bags needed at the required depth. Is the teacher's suggestion of 12 bags correct?
Read the worked answer
Area of the rectangle = 12 × 8 = 96 square meters. At a depth of 5 cm (0.05 m), one 0.05 m³ bag covers exactly 1 m², so she needs 96 bags. The teacher's 'one bag per meter of length' gives 12 bags-far too few, because it ignores the width and treats a length measure as an area measure. Twelve bags would mulch only 12 m², leaving 84 m² bare.
2. Determine whether the club can afford the correct number of bags within the $90 budget, and state what the shortfall is.
Read the worked answer
At $7 per bag, 96 bags cost 96 × $7 = $672, which is far over the $90 budget. The shortfall is $672 − $90 = $582. With $90 the club can buy at most 90 ÷ 7 ≈ 12.8, so 12 bags-coincidentally the teacher's number-which covers only 12 m². To stay in budget the club must either mulch a smaller area (about 12 m²), find cheaper mulch, or raise more funds; the full 96 m² is not affordable at this price.
3. The triangular herb bed has base 6 m and height 4 m. If the club later decides to mulch it too, how many additional bags are needed, and does that change the budget conclusion?
Read the worked answer
Area of a triangle = ½ × base × height = ½ × 6 × 4 = 12 m². At 1 m² per bag, that is 12 more bags, costing 12 × $7 = $84. Total bags would be 96 + 12 = 108, costing $756. This makes the budget problem worse, not better, so the conclusion is unchanged: the full project is well beyond $90 and requires either reduced scope or additional funding.