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 e

Question

2 months ago

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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 e

qual number of pop songs and an equal number of rock songs into each playlist. Each song will go into only one playlist.

Mathematics

1 answer:

babunello [11.8K] · Answer 1 · 2026-03-17T06:30:38+03:00

Answer:

Katherine will create at least 8 playlists. Each of these will feature 4 pop songs and 9 rock songs.

Detailed Explanation:

Katherine has a library of 32 pop songs and 72 rock songs on her mp3 player. She intends to distribute these into playlists, ensuring an equal count of pop and rock songs in each.

To determine the minimum number of playlists, we find the GCF of the two numbers provided.

For 32, we can express it as 2^5, and 72 can be described as 2^3*3^2

Thus, the GCF for the two figures is 2^3, equaling 8.

Consequently, she will generate 8 playlists, with each containing 4 pop songs and 9 rock songs.