Jen and Jacob want to put a cement deck around their pool. Use the figure below to calculate the area of the deck. If cement costs $4.75 per square foot, how much is the cost of the deck? Round to the nearest hundredth.
Width of pool is x+3
Length of pool is 3x-4
Width of deck is 3x-2
Length of deck is 2x+6
If cement costs $4.75 per square foot, how much is the cost of the deck?
area= (2x+6)(3x-2) - (3x-4)(x+3)
= 6 x^2 + 14 x -12 -[ 3x^2 +5 x -12 ]
= 3 x^2 + 9 x
You did not say what x is so
cost = 4.75(x)(3x+9)
= 14.25 (x)(x+3)
To calculate the area of the deck, we need to multiply the width and length of the deck.
Width of deck = 3x - 2
Length of deck = 2x + 6
Area of deck = (3x - 2) * (2x + 6)
To find the cost of the deck, we need to multiply the area of the deck by the cost of cement per square foot.
Cost of the deck = Area of deck * Cost per square foot
First, let's simplify the expression for the area of the deck:
Area of deck = (3x - 2) * (2x + 6)
= 6x^2 + 18x - 4x - 12
= 6x^2 + 14x - 12
Now, let's calculate the cost of the deck using the formula:
Cost of the deck = (6x^2 + 14x - 12) * $4.75
Multiply each term by $4.75:
Cost of the deck = (6x^2) * $4.75 + (14x) * $4.75 - (12) * $4.75
= $28.5x^2 + $66.5x - $57
Therefore, the cost of the deck is $28.5x^2 + $66.5x - $57. The actual value of the cost will depend on the specific value of x that is plugged into the equation.