The Utility Maximizing Rule States That "If MU_X/P_X = MU_Y/P_Y

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The Answer is If you were maximizing utility, the marginal utility per dollar of everything that you buy would be equal. That is True because if they were not equal, you should buy more of the item with the greater marginal utility per dollar and less of the item with the lower marginal utility per dollar. But as you buy more of the product with the higher marginal utility per dollar, the marginal utility of that product will fall due to the principle of diminishing marginal utility. Conversely, as you buy less of the other product, its marginal utility will rise. You continue to reallocate your purchases until the marginal utility per dollar is the same for all items purchased.
The equality of marginal utilities per dollar (MU_X/P_X = MU_Y/P_Y) implies that the ratio of prices is just equal to the ratio of marginal utilities. (P_Y/P_X = MU_Y/MU_X).

The Utility Maximizing Rule States That "If MUX/PX = MUY/PY

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The Utility Maximizing Rule States That "If MU_X/P_X = MU_Y/P_Y