Katherine can make a maximum of 8 playlists.
Each playlist will contain 4 pop songs and 9 rock songs.
Katherine's Playlist Organization
Problem: Katherine has 32 pop songs and 72 rock songs on her MP3 player.
She wants to organize them into "paulistas" (assuming these are playlists) with an equal number of pop and rock songs in each playlist.
The question asks for the greatest number of playlists she can make and the number of songs per playlist.
Solution:
Find the Greatest Common Factor (GCD):
To ensure an equal number of pop and rock songs in each playlist, we need to find the largest number that divides both 32 and 72. This is the GCD of 32 and 72.
Calculating GCD:
Factorize both numbers:
32 = 2^5
72 = 2^3 * 3^2
Take the minimum power of each common factor:
GCD(32, 72) = 2^3 = 8
Number of Playlists:
Katherine can create 8 playlists because 8 divides both 32 and 72 evenly.
Number of Songs per Playlist:
Pop: 32 songs / 8 playlists = 4 songs per playlist.
Rock: 72 songs / 8 playlists = 9 songs per playlist.
Step-by-step explanation:
The GCD of 8 represents the largest "unit" which can be used to divide both pop and rock songs equally.
Dividing the total number of songs by the GCD gives the number of songs per playlist for each genre.
Question
Katherine has 32 pop songs in 72 rock songs on her MP3 player that she will be organizing into paulista. Que want to por an erial nombre of pop sounfs and an erial nombre of rock sounfs in to each playlist. the greatest number of playlist Catherine can make is what? each of these playlist will have how many pop songs and how many rock songs?