Answer :
Answer:
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 [tex]7 (3min) = 21[/tex] song minutes.
If we call [tex]c[/tex] 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 [tex]3.5c[/tex]; therefore, we have the inequality
[tex]3.5c+21\leq 72[/tex] (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:
[tex]3.5c\leq 51[/tex]
[tex]$c\leq \frac{51}{3.5} $[/tex]
[tex]c\leq 14.47[/tex]
The maximum integer value [tex]c[/tex] can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.
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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