Final answer:
The question involves creating and solving algebraic equations to find two positive numbers where one is 3 less than twice the other and their squares differ by 24.
Step-by-step explanation:
Let's denote the two positive numbers as x and y, where y is 3 less than 2 times x (y = 2x - 3).
The difference of their squares is 24, so we write the equation x² - y² = 24. Using the fact that a² - b² = (a + b)(a - b), we rewrite the equation as (x + y)(x - y) = 24.
Substituting the expression for y, we get (x + (2x - 3))(x - (2x - 3)) = 24, which simplifies to (3x - 3)(-x + 3) = 24.
By solving for x, we find two possible values for x. Upon checking for positive solutions that also satisfy y being positive, we can determine the two numbers accordingly.