The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72 minutes long. The jazz choir records 7 songs with an average of 3 minutes per songEach symphonic choir song is an average of 3.5 minutes long. What is the maximum number of songs the symphonic choir can record?

Let x represent the number of songs the symphonic choir can record.

The album can be no more than 72 minutes long. The jazz choir records 7 songs with an average of 3 minutes per song.

Each symphonic choir song is an average of 3.5 minutes long

Hence:

(7 song * 3 minute per song) + (x song * 3.5 minute per song) ≤ 72 minute

21 + 3.5x ≤ 72

3.5x ≤ 51

x ≤ 14.6

The maximum number of songs the symphonic choir can record is 14 songs.

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The symphonic choir can record a maximum of 14 songs.

Step-by-step explanation:

We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of  song minutes.

If we call the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are ; therefore, we have the inequality

(this says the song minutes for jazz choir plus song minutes for symphonic choice cannot exceed 72 minutes )

We solve this inequality by subtracting 21 from both sides and then dividing by 3.5:

The maximum integer value can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.

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