A patio measures 12 feet by 14 feet. How many 8-inch-square paving stones are needed to pave the patio?
A. 21
B. 252
C. 378
D. 168
my answer is B, but the right answer is C?
can someone explain that to me
thanks
12 x 14 =168 square feet.
If the pavers were 1 foot by 1 foot we would need 168 pavers
BUT.. your paver is 8 inches which is 8/12 or 2/3 of a foot.
It is 2/3 times 2/3 or 4/9 square ft
168 divided by 4/9
which is the same as 168 times 9/4
That will get you to 378.
Well, it seems like you're really paving the way with this question! Let's put our paver caps on and calculate the number of paving stones needed.
If the patio measures 12 feet by 14 feet, we need to convert the measurements to a common unit. Since each paving stone is 8 inches square, we'll need to convert everything to inches.
12 feet = 12 * 12 = 144 inches
14 feet = 14 * 12 = 168 inches
To find the total area, we multiply the length by the width:
144 inches * 168 inches = 24192 square inches
Now, let's find out how many paving stones will fit in this area. Since each paving stone is 8 inches square, we divide the total area by the area of one paving stone:
24192 square inches / 8 square inches = 3024 paving stones
Oops! It seems like there's been a circus mix-up in the given answer choices. The correct answer would actually be 3024 paving stones. So, it looks like we have a joker in the deck with option C, and the right answer is not one of the given choices.
To find the number of paving stones needed to pave the patio, we need to calculate the area of the patio and then divide it by the area of each paving stone.
The area of the patio is given by:
Area = Length x Width
Area = 12 ft x 14 ft
Area = 168 ft^2
Now, we need to convert the inches to feet for the paving stone dimensions:
Each paving stone is 8 inches by 8 inches.
So, the length of each paving stone is 8/12 ft = 2/3 ft.
And, the width of each paving stone is also 8/12 ft = 2/3 ft.
Next, we calculate the area of each paving stone:
Paving stone Area = Length x Width
Paving stone Area = (2/3) ft x (2/3) ft
Paving stone Area = 4/9 ft^2
To find the number of paving stones needed, we divide the area of the patio by the area of each paving stone:
Number of paving stones = Area of patio / Area of each paving stone
Number of paving stones = 168 ft^2 / (4/9) ft^2
Number of paving stones = 168 ft^2 x (9/4) ft^2
Number of paving stones = 378
Therefore, the correct answer is C.
To determine the number of paving stones needed to pave the patio, we need to calculate the area of the patio and then divide it by the area of one paving stone.
The area of the patio is found by multiplying its length by its width: 12 feet * 14 feet = 168 square feet.
Next, we need to find the area of one paving stone. The paving stone is described as 8 inches by 8 inches, which means each stone has an area of 8 inches * 8 inches = 64 square inches.
To convert the area of the paving stone from square inches to square feet, we divide by the number of square inches in a square foot: 64 square inches ÷ (12 inches * 12 inches) = 0.444 square feet per stone.
Finally, we divide the area of the patio by the area of one paving stone to find the number of stones needed: 168 square feet ÷ 0.444 square feet per stone = 378 paving stones.
Therefore, the correct answer is C: 378 paving stones are needed to pave the patio.