Vivian has 45 songs on her MP3-player, 15 of which are alternative rock and the rest of which are rap. Malik has 60 songs on his MP3-player in the same ratio as Vivian’s songs. How many more rap songs does Malik have on his MP3-player than Vivian has on hers?
Vivian has 2/3 rap.
so, what is 2/3 of 60?
How much more is that than 2/3 of 45?
To solve this problem, we need to determine the number of rap songs on Vivian's MP3-player and the number of rap songs on Malik's MP3-player.
We know that Vivian has a total of 45 songs, and out of those, 15 are alternative rock. Thus, the remaining songs must be rap songs.
To find the number of rap songs on Vivian's MP3-player, we subtract the number of alternative rock songs from the total number of songs:
Rap songs on Vivian's MP3-player = Total songs - Alternative rock songs
Rap songs on Vivian's MP3-player = 45 - 15
Rap songs on Vivian's MP3-player = 30
Now, we need to determine the number of rap songs on Malik's MP3-player. Since the ratio of Vivian's songs remains the same, we can use proportions to find the number of rap songs on Malik's MP3-player.
The ratio of alternative rock to rap songs for Vivian is 15:30, which can be simplified to 1:2.
We know that Malik has a total of 60 songs, and we need to find the number of rap songs. Using the same ratio as Vivian's MP3-player, we set up the proportion:
Alternative rock songs on Malik's MP3-player : Rap songs on Malik's MP3-player = 1 : 2
We can set up the proportion equation:
15 : x = 1 : 2
To solve for x, we can cross-multiply and solve the equation:
15 * 2 = 1 * x
30 = x
Therefore, Malik has 30 rap songs on his MP3-player.
To find out how many more rap songs Malik has than Vivian, we subtract the number of rap songs on Vivian's MP3-player from the number of rap songs on Malik's MP3-player:
Difference in rap songs = Rap songs on Malik's MP3-player - Rap songs on Vivian's MP3-player
Difference in rap songs = 30 - 30
Difference in rap songs = 0
Therefore, Malik has 0 more rap songs than Vivian on his MP3-player.