Final answer:
The number of songs on the final CD can be found by multiplying the percentage of extra songs written and recorded with the percentage of songs removed during editing. The answer is option 4: \(\frac{x}{100} \times \frac{y}{100} \times x\) songs.
Step-by-step explanation:
To find the number of songs on the final CD, we need to consider two steps: writing and recording extra songs, and removing some during the editing process. Let's assume the band expects to put n songs on the CD. According to the given information, they write and record x% more songs than they expect to put on the CD, which means they write and record n + (x/100)n = n(1 + x/100) songs. Then, during the editing process, y% of the songs are removed, which gives us n(1 + x/100) - (y/100)n(1 + x/100) = n(1 + x/100)(1 - y/100) songs. Therefore, the answer is option 4, which is \(\frac{x}{100} \times \frac{y}{100} \times x\) songs.
If the band writes and records x% more songs than this base number, they effectively have base number of songs × (1 + x/100) songs before editing. Once y% of the songs are removed during the editing process, the band is left with base number of songs × (1 + x/100) × (1 - y/100) songs. None of the provided answer choices correctly represent this scenario, so we would need more information or different choices to find the correct answer.