Mark, jessica & nate each downloaded music from the same website. mark downloaded 10 songs in total consisting of pop, rock, & hip hop. jessica downloaded 5 times as many pop songs, twice as many rock and 3 times as many hip hop songs as mark. she downloaded 28 songs total. if nate downloaded 20 songs total with 3 times as many pop songs, 3 times as many rock songs, and the same number of hip hop songs as mark, how many songs of each type did mark download?

P + r + h = 10 <== mark
5p + 2r + 3h = 28 <== jessica
3p + 3r + h = 20 <== nate

p + r + h = 10
3p + 3r + h = 20...multiply by -1

p + r + h = 10
-3p - 3r - h = -20 (result of multiplying by -1)
add
-2p - 2r = -10

p + r + h = 10...multiply by -3
5p + 2r + 3h = 28

-3p - 3r - 3h = -30 (result of multiplying by -3)
5p + 2r + 3h = 28
add
2p - r = -2

-2p - 2r = -10
2p - r = -2
add
-3r = -12
r = -12/-3
r = 4

2p - r = -2
2p - 4 = -2
2p = -2 + 4
2p = 2
p = 1

p + r + h = 10
1 + 4 + h = 10
5 + h = 10
h = 10 - 5
h = 5

Jessica downloaded : 5p + 2r + 3h = 28
5(1) + 2(4) + 3(5) = 28
5 + 8 + 15 = 28
28 = 28 (correct)she got 5 pop, 8 rock, and 15 hip hop

Nate downloaded : 3p + 3r + h = 20
3(1) + 3(4) + 5 = 20
3 + 12 + 5 = 20
20 = 20 (correct)...he got 3 pop, 12 rock, and 5 hip hop

Mark downloaded : p + r + h = 10
1 + 4 + 5 = 10
10 = 10 (correct)he got 1 pop, 4 rock, and 5 hip hop <===

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