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
