A number x is increased by 150% of itself, resulting in a total of 500.

Think of the total as 250% of the number ($100\% + 150\% = 250\%$). Since 250% is 2.5 times the number, divide 500 by 2.5: $500 / 2.5 = 200$.

Many students calculate 150% of 500 (which is 750) or interpret 'increased by 150%' as the final number being 150% of the original instead of $100\% + 150\% = 250\%$.

This concept of 'percentage base' is identical to 'Successive Percentage' and 'Profit and Loss' problems where adding a margin or markup follows the same logic: $\text{New Value} = \text{Original} \times (1 + \frac{\text{Rate}}{100})$.