Solve the following word problems

Question

Shannon is building a deck around her square swimming pool. Let d = the width of the deck.

The pool is 23 ft

1. Given the diagram to the right, write a polynomial that represents the total area of the deck and pool.
2. Find the combined area if the width of the deck is 12 feet.
3. If the pool is 5 feet deep, how much would it cost to fill it if water is $1.50 for 1000 gallons? Remember that 1 gallon 0.134 ft^3. Round your answer to the nearest cent

Answer 1

(1)

then the side measures of the square become 23 + 2d

the area is then (2d + 23)(2d + 23) = 4d^2 + 92d + 529

(2) for d=12, the total area is (2*12+23)^2 = (24+23)^2 = 47^2 = 2209..

OR you can do 4*12^2 + 92*12 + 529 = 4*144+ 92*12 + 529 = 2209

(3) the volume of the pool is 23*23*5 = 2645 cubic feet

2645 / 0.134 = 19738.805+..... gallons are needed.

$1.50 per 1000 gallons means

19.738805... * 1.50 = $29.61 + tax