Question

Lots of points!!!!!

Answer 1

Answer:

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

Step-by-step explanation:

Let us assume that the number of pop songs be x .

Let us assume that the number of rock songs be y .

Let us assume the the number of hip hop songs be z .

As given

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

Than the equation becomes

x + y + z = 10

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

Number of pop songs jessica download = 5x

Number of rock songs jessica download = 2y

Number of hip hop songs jessica download = 3z

She downloaded 28 songs total.

Than the equation becomes

5x + 2y + 3z = 28

As given

If Nate downloaded 20 songs total .

Three times as many pop songs, three times as many rock songs, and the same number of hip hop songs as Mark .

Number of pop songs Nate download = 3x

Number of rock songs Nate download = 3y

Number of hip hop songs Nate download = z

Than the equation becomes

3x + 3y + z = 20

Thus the three equations are .

x + y + z = 10

5x + 2y + 3z = 28

3x + 3y + z = 20

Multiply x + y + z = 10 by 2 and subtracted from 5x + 2y + 3z = 28 .

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

3x + z = 8

Multiply x + y + z = 10 by 3 and subtracted from 3x + 3y + z = 20  .

3x - 3x + 3y - 3y + z - 3z = 20 -30

-2z = -10

$z = \frac{-10}{-2}$

z = 5

Put in the equation 3x + z = 8 .

3x + 5 = 8

3x = 8 - 5

$x = \frac{3}{3}$

x = 1

Put x = 1 , z = 5 in the equation x + y + z = 10 .

1 + 5 + y = 10

6 + y = 10

y = 10 - 6

y = 4

Thus

Number of pop songs mary download = 1

Number of rock songs mary download = 4

Number of hip hop songs mary download = 5

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

Answer 2

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