220,149 views
23 votes
23 votes
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 schgs, 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?

User Mrcrowl
by
2.8k points

2 Answers

18 votes
18 votes

Answer:

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Explanation:

Let

x = number of pop song downloaded by Mike

y = number of rock song downloaded by Mike

z = number of hip song downloaded by Mike

Mark downloaded 10 songs in total consisting of pop, rock, and hip hop

Mark:

x + y + z = 10

Jessica downloaded five times as many pop songs, twice as many rock schgs, and three times as many hip hop songs as Mark. She downloaded 28 songs total.

Jessica:

5x + 2y + 3z = 28

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.

Nate:

3x + 3y + z = 20

The following system of equations represents their music choices

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Explanation:

User Diaz
by
2.9k points
28 votes
28 votes

Answer:

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

Explanation:

Let

x = number of pop song downloaded by Mike

y = number of rock song downloaded by Mike

z = number of hip song downloaded by Mike

Mark downloaded 10 songs in total consisting of pop, rock, and hip hop

Mark:

x + y + z = 10

Jessica downloaded five times as many pop songs, twice as many rock schgs, and three times as many hip hop songs as Mark. She downloaded 28 songs total.

Jessica:

5x + 2y + 3z = 28

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.

Nate:

3x + 3y + z = 20

The following system of equations represents their music choices

Mark:

x + y + z = 10

Jessica:

5x + 2y + 3z = 28

Nate:

3x + 3y + z = 20

User Onosendi
by
2.5k points
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