Final answer:
An equation representing the future ages of Bill and Ada was derived from the statement given. Using x for Ada's age and y for Bill's age, the equation y + 19 = 2(x + 19) simplifies to y = 2x - 19, which rearranges to option b, x - 2y = -19.
Step-by-step explanation:
The student wants to form an equation based on the statement: 'In 19 years, Bill will be twice as old as Ada.' Let's use x to represent Ada's current age and y to represent Bill's current age. In 19 years, Ada's age will be x + 19 and Bill's age will be y + 19. According to the statement, Bill will be twice as old as Ada in 19 years, which gives us the equation y + 19 = 2(x + 19). Simplifying this equation, we subtract 19 from both sides to get y = 2x + 38 - 19, which simplifies to y = 2x - 19.
The correct answer is b. x - 2y = -19, as it represents the rearrangement of the simplified equation.
To see why, let's rearrange y = 2x - 19 by subtracting 2x from both sides of the equation, which yields -2x + y = -19. Multiplying the entire equation by -1 to make the x coefficient positive, we obtain x - 2y = -19.