Question

Mark, Jessica, and Nate each downloaded music from the same website. Mark downloaded 10 songs in total consisting of pop, rock, and hip hop. Jessica downloaded five times as many pop songs, twice as many rock songs, and three times as many hip hop songs as Mark. She downloaded 28 songs total. Nate downloaded 20 songs total with three times as many pop songs, three times as many rock songs, and the same number of hip hop songs as Mark. Which system of equations represents their music choices?

x + y + z = 10
5x + 2y + 3z = 28
3x + 3y + z = 20

x + y + z = 10
2x + 5y + 3z = 28
3x + 3y + z = 20

x + y + z = 10
5x + 2y + 3z = 28
3x + 3y + 3z = 20

x + y + z = 10
2x + 3y + 5z = 28
x + 3y + 3z = 20

Answer 1

Let's say x is the number of pop songs that Mark downloaded
and y is the number of rock songs that Mark downloaded
and z is the number of hip hop songs that Mark downloaded

He downloaded a total of 10 songs
The first equation would be
x + y + z = 10

Answer 2

Now Jessica downloaded 5 times as many pop songs as Mark
and 2 times as many rock songs as Mark
and 3 times as many hip hop songs as Mark

She downloaded a total of 28 songs

Mark downloaded 'x' number of pop songs which means Jessica downloaded 5 times x or 5x
Mark downloaded 'y' number of rock songs which means Jessica downloaded 2 times y or 2y
Similarly, do that for hip hop songs

Then you add them all up and set it equal to 28

Answer 3

That will be your second equation in the system of equations

Answer 4

Finally, Nate downloaded 3 times as many pop songs as Mark
and 3 times as many rock songs as Mark
and the same number of hip hop songs as Mark

He downloaded a total of 20 songs

Mark has x number of pop songs so Nate has 3 times x
... and so on

and it equals to a total of 20 songs

That's how you get your third equation

Answer 5

Does that help? Are you able to figure out what the final answer is

Answer 6

Yes i found out the answer it is the first one, thank you this helped!

Answer 7

That's correct. You're welcome!