Question

Katherine has 32 pop songs and 72 rock songs on her mp3 player that she will be organizing into playlists. She wants to put an equal number of pop songs and an equal number of rock songs into each playlist. Each song will go into only one playlist.

Answer 1

Katherine will make minimum 8 playlists. Each playlist will contain 4 pop songs and 9 rock songs.

Explanation:

We have been given that Katherine has 32 pop songs and 72 rock songs on her mp3 player. She is willing to organizing the songs into playlists such that there are equal number of pop songs and an equal number of rock songs into each playlist.

We can find the minimum number of playlists by finding GCF of the given two numbers.

We can write 32 = 2^5 and we can write 72 = 2^3*3^2

Therefore, GCF of the two numbers is 2^3 = 8.

Hence, she will be making total 8 playlists where each playlist will contain 4 pop songs and 9 rock songs.