Question

a landscape company wants to plant lawn seed. a 20 lb. bag of lawn seed will cover up to 420 sq. ft. of grass and costs $49.98 plus the 8% sales tax. a scale drawing of a rectangular yard is given. the length of the longest side is 100 ft, and the shorter side is 90 ft. the house, driveway, sidewalk, garden areas, and utility pad are shaded. the unshaded area has been prepared for planting grass. on the picture below every 1 square of the graph paper is equal to 5 square feet. calculate the area that is to be covered by grass and determine how many 20 lb. bags of lawn seed should be ordered, and what is the cost? remember that you cannot buy a portion of a bag. area to be covered by grass: ft² bags will cost $ including tax.

Explanation:

Step1: Calculate total yard area

The yard is rectangular with length $l = 100$ ft and width $w=90$ ft. The total area of the yard $A_{total}=l\times w=100\times90 = 9000$ square - feet.

Step2: Calculate area per square on graph - paper

Each square on the graph - paper represents 5 square feet.

Step3: Count shaded squares and find shaded area

(Assume we count the shaded squares on the graph - paper. Let's say we count $n$ shaded squares. Without the actual count from the image, we'll continue the general process). The shaded area $A_{shaded}=5n$ square feet.

Step4: Calculate area to be covered by grass

$A = A_{total}-A_{shaded}$.

Step5: Determine number of bags

Let $A$ be the area to be covered by grass. The number of bags $N=\lceil\frac{A}{420}
ceil$ (we use the ceiling function because we can't buy a fraction of a bag).

Step6: Calculate cost per bag with tax

The cost of one bag before tax is $C_0 = 49.98$ dollars. The tax rate is $r = 0.08$. The cost of one bag with tax $C = C_0(1 + r)=49.98\times(1 + 0.08)=49.98\times1.08=53.9784\approx53.98$ dollars.

Step7: Calculate total cost

The total cost $T = N\times C$.

Let's assume we counted 1800 square - feet of shaded area (for demonstration purposes). Then:

Step4 (with assumed value):

$A=9000 - 1800=7200$ square feet.

Step5 (with assumed value):

$N=\lceil\frac{7200}{420}
ceil=\lceil17.14
ceil = 18$ bags.

Step7 (with assumed value):

$T = 18\times53.98=971.64$ dollars.

Answer:

Area to be covered by grass: 7200 (assuming shaded area of 1800 square feet)
Number of bags: 18
Total cost: 971.64