Final answer:
To find the value of x when the ratio 125:x is equivalent to the ratio x²:125, we set up an equation based on these ratios and simplify to x² = 125x. Dividing both sides by x (assuming x is non-zero) gives us x = 125.
Step-by-step explanation:
The student has been given a proportional relationship where the ratio 125:x is equivalent to the ratio x²:125. To find the value of x, we need to set up an equation based on the given ratios. After setting up the equation, it simplifies into a quadratic equation that could be rewritten as x² - 125x + 125² = 0 or x² = 125x. Since we are only looking for a positive value of x, we can divide both sides by x (given x is not zero) and find that x = 125.