Question

alans rectangular flower bed measures 122 cm long and 63 cm wide. he wants to cover the flower bed in mulch. he knows the area each bag of mulch covers, but only in square feet. (a) find the area of alans flower bed in square feet. do not round intermediate computations and round your final answer to two decimal places. use the table of conversion facts, as needed. (b) alan wants to cover his flower bed with mulch. he doesnt have any to begin with and he cant buy partial bags of mulch. each bag of mulch covers 2.2 ft². how many whole bags of mulch does alan need to buy to completely cover his flower bed? (c) if each bag of mulch costs $3.64, how much will he need to spend on mulch? write your answer to the nearest cent. note that ≈ means \is approximately equal to\. for this problem, treat ≈ as if it were =. conversion facts for length: 1 inch (in) = 2.54 centimeters (cm), 1 foot (ft) = 30.48 centimeters (cm), 1 yard (yd) ≈ 0.91 meters (m), 1 mile (mi) ≈ 1.61 kilometers (km)

Explanation:

Step1: Convert centimeters to feet for flower - bed dimensions

First, convert the length and width of the flower - bed from centimeters to feet. Given 1 foot = 30.48 centimeters.
The length of the flower - bed $l = 122$ cm. So, $l=\frac{122}{30.48}\text{ ft}\approx4.0039\text{ ft}$.
The width of the flower - bed $w = 63$ cm. So, $w=\frac{63}{30.48}\text{ ft}\approx2.0669\text{ ft}$.

Step2: Calculate the area of the flower - bed

The area of a rectangle $A = l\times w$.
$A=(4.0039)\times(2.0669)\text{ ft}^2\approx8.27\text{ ft}^2$.

Step3: Determine the number of mulch bags

Each bag of mulch covers $2.2\text{ ft}^2$.
The number of bags $n=\frac{A}{2.2}=\frac{8.27}{2.2}\approx3.76$. Since we can't buy partial bags, we need to round up to 4 bags.

Step4: Calculate the total cost

Each bag costs $\$3.64$.
The total cost $C = 4\times3.64=\$14.56$.

Answer:

(a) $8.27$
(b) 4
(c) $\$14.56$