Joanie's mistake lies in her misunderstanding of how to properly apply the multiplication property of equality, particularly at the first step of her reasoning. The correct approach to solve the proportion involves recognizing that you can apply cross multiplication directly from the proportion.
Specifically, Joanie's assertion that "if you multiply both sides of the equation by x, you get 3* = 75" is incorrect because she did not properly set up the proportion at the start. In a proportion formatted as \( \frac{3}{x} = \frac{75}{1} \), cross multiplying should yield \( 3 \times 1 = 75 \times x \), leading to \( 3 = 75x \).
Instead, Joanie's steps led to the incorrect equation \( 50x = 75 \), which is not reflective of the original proportion.
Thus, the correct answer is:
• She assumed that the multiplication property of equality allows her to multiply both sides of the equation \( \frac{3}{x} = 75 \) incorrectly, leading to the wrong interpretation of the equation.