Question

A radio 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?

Answer 1

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

Answer: 

48 Rock, 144 Pop and 80 Hip-hop