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, and three times as many hip hop songs as Mark. She downloaded 28 songs total. If 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, how many songs of each type did Mark download?

Answer 1

You can use the information in the question get the equations:

Mark - 10=p+r+h [p=pop, r=rock, h=hip hop]
Jess - 28 =5p+2r+3h
Nate - 20=3p+3r+h

Multiplying Mark equation by three (giving 30=3p+3r+3h) and taking away Nate's equation from this leaves a new equation 10=2h, so h=5

You can then multiply mark original equation again, but by 2 (giving 20=2p+2r+2h) and subtract this from Jess equation (giving 3p+h=8) and we know h=5, so 3p=3 and p=1

Answer 2

Mark downloaded 2 pop songs, 5 rock songs, and 3 hip hop songs.

Mark downloaded 3 pop songs, 2 rock songs, and 5 hip hop songs.

Mark downloaded 4 pop songs, 2 rock songs, and 4 hip hop songs.

Mark downloaded 1 pop songs, 4 rock songs, and 5 hip hop songs.