Aradio station plays a total of 272 pop, rock, and hip-hop songs during a day. the number of pop songs is 3 times the number of rock songs. the number of hip-hop songs is 32 more than the number of rock songs. how many of each type of song does the radio station play?

Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.

i) 
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"

means that : P+R+H=272

ii) 
"The number of pop songs is 3 times the number of rock songs. "

so, P=3R

iii)
"The number of hip-hop songs is 32 more than the number of rock songs."

means: H=32+R

iv)

since both P and H can be written in terms of R, we have:

P+R+H=272

(3R)+R+(32+R)=272

3R+R+32+R=272

5R+32=272

5R=272-32=240

R=240/5=48

vi) 

thus: P=3R=3*48=144,    H=32+R= 32+48=80

 

48 Rock, 144 Pop and 80 Hip-hop