Final answer:
To find the width of the walkway around a pool, subtract the area of the pool from the total area of the walkway and the pool combined. Use the dimensions of the larger rectangle (7x + 2w) and (9x + 2w), where w is the width of the walkway, and the dimensions of the smaller rectangle (the pool) to set up an equation. Solve the equation to find the width of the walkway.
Step-by-step explanation:
To find the width of the walkway, we need to subtract the area of the pool from the total area of the walkway and the pool combined. The total area of the walkway and the pool combined can be calculated by finding the area of the larger rectangle and subtracting the area of the smaller rectangle (the pool). The dimensions of the larger rectangle are (7x + 2w) and (9x + 2w), where w is the width of the walkway. The dimensions of the smaller rectangle (the pool) are 7x and 9x. Therefore, the total area of the walkway and the pool combined is (7x + 2w)(9x + 2w), and the area of the pool is 7x * 9x = 63x^2.
Given that the total area of the pool is 483, we have the equation:
(7x + 2w)(9x + 2w) - 63x^2 = 483
Simplifying this equation, we get:
63x^2 + 18wx + 4w^2 - 63x^2 = 483
18wx + 4w^2 = 483
Setting this equation equal to 0, we can solve for w using algebraic methods or by factoring.