To determine the total cost of mulch needed to cover a rectangular garden, we need to follow several steps:
1. Calculate the volume of mulch needed:
- First, convert the depth from inches to feet. We know 3 inches is equal to [tex]\( \frac{3}{12} \)[/tex] feet, which simplifies to 0.25 feet.
- The garden has dimensions 3 feet (width) and 10 feet (length).
- The volume [tex]\( V \)[/tex] of mulch needed can be calculated using the formula for the volume of a rectangular prism: [tex]\( V = \text{length} \times \text{width} \times \text{depth} \)[/tex].
Substituting the values:
[tex]\[
V = 10 \, \text{feet} \times 3 \, \text{feet} \times 0.25 \, \text{feet} = 7.5 \, \text{cubic feet}
\][/tex]
2. Determine the number of bags of mulch required:
- Each bag contains 2 cubic feet of mulch.
- To find out how many bags are needed, divide the total volume of mulch by the volume of one bag:
[tex]\[
\text{Number of bags} = \frac{7.5 \, \text{cubic feet}}{2 \, \text{cubic feet per bag}} = 3.75 \, \text{bags}
\][/tex]
- Since we cannot purchase a fraction of a bag, we'll round up to the nearest whole number, so we need 4 bags.
3. Calculate the total cost:
- Each bag costs \[tex]$3.66.
- Multiply the number of bags by the cost per bag to get the total cost:
\[
\text{Total cost} = 4 \, \text{bags} \times \$[/tex]3.66 \, \text{per bag} = \[tex]$14.64
\]
Therefore, the minimum number of bags required to cover the garden will cost \$[/tex]14.64, which corresponds to option 3) [tex]$\$[/tex] 14.64$.
