Final answer:
To determine how many songs are played during a 2-hour and 15-minute music broadcast that features 3-minute and 6-minute songs, calculate the total minutes (135) and divide by the song lengths, leading to a range of possible songs played between 22 and 45 total.
Step-by-step explanation:
The question asks us to calculate how many songs will be played during a 2-hour and 15-minute music broadcast where songs are either 3 minutes or 6 minutes long. First, we convert the total broadcast time into minutes: 2 hours multiply by 60 minutes per hour plus 15 minutes equals 135 minutes. We can set up the problem as an equation where x is the number of 3-minute songs and y is the number of 6-minute songs:
3x + 6y = 135
Assuming an extreme where all songs are 3 minutes, we divide 135 by 3, finding that 45 songs could be played if they were all 3 minutes long. Conversely, if all songs were 6 minutes long, 135 divided by 6 gives us 22.5, which isn't possible since you can't play half a song, so 22 songs would be the maximum in that scenario. The actual number of played songs will likely be a combination of the two lengths, so it will fall between 22 and 45 songs.