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. Write a system of THREE linear equations to represent this situation.

Answer 1

x + y + z = 272 - - - - - - (1)

x = 3y - - - - - - - - - - - - - (2)

z = 32 + y - - - - - - - - - - (3)

Explanation:

Let :

Number of pop songs = x

Number of rock songs = y

Number of hophops = z

Sum of the three types of songs = 272

x + y + z = 272 - - - - - - (1)

Pop is 3 times Rock :

x = 3y - - - - - - - - - - - - - (2)

Hiphop is 31 more than rock

z = 32 + y - - - - - - - - - - (3)