Final answer:
The width of the wooden deck surrounding the pool is 15 feet. This was determined by setting up an equation for the total area including the deck, expanding and simplifying it, and then solving for the variable representing the deck width.
Step-by-step explanation:
The question asks us to find the width of the deck that surrounds a rectangular pool, given the dimensions of the pool and the total area including the deck. To solve this problem, we will use the formula for the area of a rectangle and a system of equations.
Let the width of the deck be represented as x feet. The length and width of the pool are given as 40 ft and 30 ft, respectively. The total area including the deck is 4200 square feet. The length and width of the total area including the deck would then be (40 + 2x) and (30 + 2x), respectively.
The area of the total space is represented by A = (length + 2x) * (width + 2x). Substituting the given values, we get 4200 = (40 + 2x)(30 + 2x). Expanding this, we get 4200 = 1200 + 80x + 60x + 4x2, simplifying to 4x2 + 140x - 3000 = 0. Dividing by 4, we have x2 + 35x - 750 = 0. By factoring, (x + 50)(x - 15) = 0. So, x can be -50 or 15. Since the width can't be negative, x = 15 feet is the width of the deck.