# Number of songs sung.

There were 750 people when the first song was sung. After each song, 50 people are leaving the hall. How many songs are sung to make them zero?

The answer is 16, I am unable to understand it. I am getting 15 as the answer. Please explain.

• Why are you yelling at us? – Cameron Buie Oct 19 '12 at 11:09

I wrote it all out to make sure that I wasn't missing a song, but I got 15 too. My best guess is that the question is not worded well, and by "when the first song was sung," they are implying that 750 people were still there at the end of the first song and people started leaving "after each [following] song". This would make the following result:

After 1 song - 750 people remaining
2 songs - 700 people remaining
3 - 650
4 - 600
5 - 550
6 - 500
7 - 450
8 - 400
9 - 350
10 - 300
11 - 250
12 - 200
13 - 150
14 - 100
15 - 50
16 - 0

So this would be ((750 people) - (50 people per song)*(n-1 songs)), but this is contingent on the assumption that nobody left after the first song.

750-50=700 people remain after the 1st song is sung, that is 50 people leave after each and every song;

700-50=650 people remain after the 2nd song is sung;

600 people remain after the 3rd;

550 people remain after the 4th;

500 people remain after the 5th;

450 people remain after the 6th;

400 people remain after the 7th;

350, 8th;

300, 9th;

250, 10th;

200, 11th;

150, 12th;

100, 13th;

50, 14th;

0 people remain after the 15th song is sung.

I see no reason for people to remain only during the 1st song and leave afterwards in such a regular pattern, I therefore dispute the answer given as 16.

Listen to the question carefully: "There were $750$ people when the first song was sung"

First song was already sung $+1$;

remaining people is $750$.

$750/50=15$;

Answer is $15+1=16$