Question

john built a compost bin in the shape of a rectangular prism. the bin is 6 ft long, 2 ft wide, and 4 ft deep. after the compost cycle is complete, the bin will be full of potting soil that john can sell at a farmers market. the potting soil will be packaged in bags. the amount of soil each bag can hold is known in cubic inches. (a) find the volume of the compost bin in cubic inches. use the table of conversion facts, as needed. (b) john is going to put the potting soil in bags. each bag holds 695 in³ of the soil. he is going to bag up as much soil as possible, but he wont partially fill any bags. how many whole bags will he fill? (c) the bags will sell for $6.19 each. if john sells all the bags, how much money will he collect? conversion facts for length: 1 foot (ft) = 12 inches (in), 1 yard (yd) = 3 feet (ft), 1 yard (yd) = 36 inches (in)

Explanation:

Step1: Convert the dimensions of the bin to inches

First, convert the length, width and depth of the bin from feet to inches.
Length: $6$ ft, since $1$ ft = $12$ inches, $6$ ft = $6\times12 = 72$ inches.
Width: $2$ ft, so $2$ ft = $2\times12=24$ inches.
Depth: $4$ ft, so $4$ ft = $4\times12 = 48$ inches.

Step2: Calculate the volume of the bin

The volume $V$ of a rectangular - prism is given by $V=l\times w\times h$.
$V = 72\times24\times48$
$V=72\times1152$
$V = 82944$ in³

Step3: Find the number of bags

To find the number of bags, divide the total volume of the bin by the volume of each bag.
Number of bags $n=\frac{82944}{695}\approx119.34$
Since we can't have partially - filled bags, the number of whole bags is $119$.

Step4: Calculate the total money

If each bag sells for $\$6.19$, then the total money $M$ is the number of bags times the price per bag.
$M = 119\times6.19$
$M=119\times(6 + 0.19)$
$M=119\times6+119\times0.19$
$M = 714+22.61$
$M = 736.61$

Answer:

(a) $82944$ in³
(b) $119$ bags
(c) $\$736.61$