1. **Problem statement:** Claudia spends $x$ percent of her monthly work time on the project "Customer Survey" for the first $a$ months, and $y$ percent for the remaining $b$ months of the year. We want to find the overall percentage of her work time spent on the project during the entire year. 2. **Given:** - Total months in a year: 12 - First period months: $a$ - Second period months: $b$ - Percentage time in first period: $x$% - Percentage time in second period: $y$% 3. **Key rule:** Since total work time is the same each month, the overall percentage is the weighted average of the two percentages, weighted by the number of months. 4. **Formula:** $$\text{Overall percentage} = \frac{a \times x + b \times y}{12}$$ 5. **Explanation:** - Multiply the percentage $x$ by the number of months $a$ to get total percentage-months for the first period. - Multiply the percentage $y$ by the number of months $b$ for the second period. - Add these two results. - Divide by total months 12 to get the average percentage over the year. 6. **Check other options:** - Dividing by 100 is incorrect because percentages are already out of 100. - Expressions involving $a \times b$ or $x \times y$ do not represent weighted averages. 7. **Final answer:** $$\boxed{\frac{a \times x + b \times y}{12} \text{ percent}}$$