Final answer:
To find x when y varies directly with x and y=3/16, we first determine the constant of variation from the given values y=14 when x=18, resulting in k=7/9. We then use this constant to calculate x, which ends up being approximately 0.241, an answer not matching any of the provided options.
Step-by-step explanation:
Since y varies directly with x, we can write this relationship as y = kx, where k is the constant of variation. We are given that y=14 when x=18, so we can use this information to find the constant k by solving 14 = k * 18. This gives us k = 14/18, which simplifies to k = 7/9.
Now, to find x when y=3/16, we substitute k and y into the equation: 3/16 = (7/9)*x. Solving for x gives us x = (3/16) * (9/7) which is x = 27/112. This fraction does not match any of the options provided, but as we need to provide the correct answer, we can simplify this fraction to its decimal equivalent which is approximately x = 0.241.
It appears there may be a typographical error in the question, as none of the answer choices match the correct answer derived through our calculations. Please verify the question and answer options for any mistakes. If this solution does not match the available options due to an error in the question setup, please consult with the instructor or source of the question for clarification.