The statement "the price for different pounds of potatoes costs one-fourth as much per pound as mangoes" can be translated into an equation.
If \( x \) represents the price of mangoes per pound and \( y \) represents the price of potatoes per pound, then the price of potatoes is one-fourth the price of mangoes. This relationship can be expressed as:
\[ y = \frac{1}{4}x \]
Thus, the correct equation that represents the relationship between the price of potatoes \( y \) and the price of mangoes \( x \) is:
\[ y = \frac{1}{4}x \]