a dog park has a length of 8 1/4 yards and the width of 25 1/2 yards. The fencing that completely surrounds the park cost 12$ a yard. Each grass sod that covers the entire park cost 8$. What was the total cost of fencing and the sod. Explain step-by-step
To calculate the cost of fencing, we need to find the perimeter of the dog park. The formula for finding the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the length of the park is 8 1/4 yards and the width is 25 1/2 yards, we can substitute these values into the formula:
Perimeter = 2(8 1/4 + 25 1/2)
To add fractions, we need a common denominator, which in this case is 2. Converting the mixed numbers to improper fractions, we get:
Perimeter = 2(33/4 + 51/2)
Next, we need to find a common denominator between 4 and 2, which is 4. Now we can add the fractions:
Perimeter = 2(33/4 + 102/4)
Perimeter = 2(135/4)
Now, multiply 2 by each fraction numerator:
Perimeter = (2/1) * (135/4)
Calculate the multiplication:
Perimeter = 270/4
Next, divide the numerator by the denominator:
Perimeter = 67.5
Therefore, the perimeter of the dog park is 67.5 yards.
Now, to find the total cost of the fencing, we need to multiply the perimeter by the cost per yard, which is $12:
Total cost of fencing = 67.5 yards * 12$/yard
Calculate the multiplication:
Total cost of fencing = $810
Now, let's calculate the cost of the grass sod. We need to find the area of the dog park, which is given by the formula:
Area = length * width
Given that the length is 8 1/4 yards and the width is 25 1/2 yards, we can substitute these values into the formula:
Area = 8 1/4 * 25 1/2
Again, convert the mixed numbers to improper fractions:
Area = 33/4 * 51/2
Multiply the numerators:
Area = (33 * 51) / (4 * 2)
Area = 1683 / 8
Now, divide the numerator by the denominator:
Area = 210.375
Therefore, the area of the dog park is 210.375 square yards.
Now, to find the total cost of the grass sod, we need to multiply the area by the cost per sod, which is $8:
Total cost of grass sod = 210.375 square yards * 8$/yard
Calculate the multiplication:
Total cost of grass sod = $1683
Finally, to find the total cost of the fencing and the sod, we add the cost of the fencing to the cost of the grass sod:
Total cost = $810 + $1683
Total cost = $2493
Therefore, the total cost of the fencing and the sod for the dog park is $2493.