1. **Stating the problem:** "Polovičné číslo trojciferného čísla je o 88 menšie ako jeho tretina. Určite číslo." 2. **Define the variable:** Let the three-digit number be $x$. 3. **Write the equation from the problem statement:** Half of the number is 88 less than one third of the number: $$\frac{x}{2} = \frac{x}{3} - 88$$ 4. **Solve the equation:** Multiply both sides by 6 (the least common multiple of 2 and 3) to clear denominators: $$6 \times \frac{x}{2} = 6 \times \left(\frac{x}{3} - 88\right)$$ $$3x = 2x - 528$$ 5. **Isolate $x$:** $$3x - 2x = -528$$ $$x = -528$$ 6. **Interpretation:** The solution $x = -528$ is a three-digit number but negative. The problem does not specify positive only, so $-528$ satisfies the equation. 7. **Verification:** Half of $-528$ is $-264$. One third of $-528$ is $-176$. Check if half is 88 less than one third: $$-264 = -176 - 88$$ $$-264 = -264$$ True. **Final answer:** $$x = -528$$