Question

joses rectangular flower bed measures 121 cm long and 89 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 joses 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.
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)
note that ≈ means \is approximately equal to\. for this problem, treat ≈ as if it were =
(b) jose 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 1.7 ft². how many whole bags of mulch does jose need to buy to completely cover his flower bed?
(c) if each bag of mulch costs $3.47, how much will he need to spend on mulch? write your answer to the nearest cent.

Explanation:

Step1: Calculate area in square - centimeters

The area $A$ of a rectangle is given by $A = l\times w$, where $l = 121$ cm and $w = 89$ cm. So $A=121\times89 = 10769$ $cm^{2}$.

Step2: Convert square - centimeters to square - feet

We know that $1$ foot = $30.48$ cm, so $1$ square - foot = $(30.48)^{2}$ $cm^{2}=929.0304$ $cm^{2}$.
To convert the area from square - centimeters to square - feet, we divide the area in square - centimeters by the number of square - centimeters in a square - foot. So $A_{ft^{2}}=\frac{10769}{929.0304}\approx11.59$ $ft^{2}$.

Step3: Determine the number of bags

Each bag covers $1.7$ $ft^{2}$. To find the number of bags $n$, we divide the total area by the area covered by each bag: $n=\frac{11.59}{1.7}\approx6.82$. Since we can't buy partial bags, we need to round up to the next whole number. So $n = 7$ bags.

Step4: Calculate the total cost

Each bag costs $\$3.47$. The total cost $C$ is the number of bags times the cost per bag. So $C = 7\times3.47=\$24.29$.

Answer:

(a) $11.59$
(b) $7$
(c) $24.29$