To determine the maximum number of playlists James can create with an equal number of sad and upbeat songs, we will find the highest common factor (HCF) of the number of sad songs (12) and the number of upbeat songs (40).
First, we find the factors of each number:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Now, we identify the common factors: 1, 2, and 4.
The highest common factor is 4. This means James can create a maximum of 4 playlists, with the same number of sad and upbeat songs in each.
Next, we calculate how many sad and upbeat songs would be in each playlist:
- For 4 playlists from 12 sad songs: 12 sad songs / 4 playlists = 3 sad songs per playlist.
- For 4 playlists from 40 upbeat songs: 40 upbeat songs / 4 playlists = 10 upbeat songs per playlist.
Thus, the maximum number of playlists he can create is 4 playlists.