Math Word Problem

Question

Four girls sang songs in a concert in trios, with one girl sitting out each song. Hannah sang 7 songs, which was more than any other girl. Mary sang 4 songs which was fewer than any other girl. How many songs did the girls sing?

Answer 1

Since the girls sang songs in trios, the sum of the songs sang by all four girls must be a multiple of 3.  

 

The 2 unidentified girls must have each sang 5 or 6 songs, so the sum of the songs sang by them must be 10, 11 or 12.  

 

The sum of the songs sang by Hannah and Mary is 11.  

 

So the sum of the songs sang by all four girls must be 21, 22 or 23.  The only 1 of these numbers that is a multiple of 3 is 21.  

 

So the sum of all the songs sang is 21  ==> there were 7 songs sang in trios.