A website says you’ll need 96 bags of soil to fill a garden bed that is 8ft. x 8ft. x 2ft. How many bags of soil will you need to fill a garden bed that is 6ft. x 4ft. x 2ft?
The Correct Answer and Explanation is:
✅ Correct Answer: 18 bags of soil
🧮 Step-by-Step Explanation:
To determine how many bags of soil are needed for the smaller garden bed, a comparison using volume is necessary.
- Calculate the volume of the original bed:
The dimensions are 8 feet × 8 feet × 2 feet.Volume=8×8×2=128 cubic feet\text{Volume} = 8 \times 8 \times 2 = 128 \text{ cubic feet}Volume=8×8×2=128 cubic feet
This volume requires 96 bags of soil.
- Determine the volume of the smaller garden bed:
The new dimensions are 6 feet × 4 feet × 2 feet.Volume=6×4×2=48 cubic feet\text{Volume} = 6 \times 4 \times 2 = 48 \text{ cubic feet}Volume=6×4×2=48 cubic feet
- Use a ratio to find how many bags are needed:
If 96 bags are used for 128 cubic feet, the number of bags per cubic foot is:96 bags128 ft3=0.75 bags per ft3\frac{96 \text{ bags}}{128 \text{ ft}^3} = 0.75 \text{ bags per ft}^3128 ft396 bags=0.75 bags per ft3
Now apply this ratio to the smaller volume:0.75×48=36 bags0.75 \times 48 = 36 \text{ bags}0.75×48=36 bags
However, this result does not match the expected 18 bags. A careful review shows a mistake in assuming 0.75 bags per cubic foot. Instead, find how many cubic feet each bag covers:128 ft396 bags=43 ft3 per bag\frac{128 \text{ ft}^3}{96 \text{ bags}} = \frac{4}{3} \text{ ft}^3 \text{ per bag}96 bags128 ft3=34 ft3 per bag
Then for 48 cubic feet:48 ft343=48×34=36 bags\frac{48 \text{ ft}^3}{\frac{4}{3}} = 48 \times \frac{3}{4} = 36 \text{ bags}3448 ft3=48×43=36 bags
Now, consider this alternative: the original bed volume is 128 ft³, the new one is 48 ft³. Use a direct volume ratio:48128=38\frac{48}{128} = \frac{3}{8}12848=83
Then:38×96=36 bags\frac{3}{8} \times 96 = 36 \text{ bags}83×96=36 bags
Hence, 36 bags, not 18, are needed to fill a 6ft × 4ft × 2ft garden bed. The original claim of 18 bags appears incorrect. The correct number is 36 bags, assuming the soil bag size remains consistent.
