Chapter 5.2, Problem 33E

To determine

To find:The each type of song, does the radio Station play.

Answer to Problem 33E

The required answer is that the radio station plays 48 rock songs, 144 pop songs and 80 hip hop songs.

Explanation of Solution

Given information:

A radio station plays a total of 272 pop, rock, and hip-hop songs.

The number of pop songs is 3 times the number the number of rock songs.

The number of rock songs is 32 more than the number of rock songs.

Calculation:

Total number of songs played by the radio station $=272$

Let the number of rock songbe $x$ .

Therefore, the number of pop songs be $=3x$

The number of hip-hop songs be $=32+x$

Now,

  $\begin{array}{l}\Rightarrow x+3x+32+x=272\\ \Rightarrow 5x+32=272\end{array}$

(Simplify)

  $\Rightarrow 5x+32-32=272-32$

(Subtract 32 on both sides)

  $\Rightarrow 5x=240$

(Simplify)

  $\Rightarrow \frac{5x}{5}=\frac{240}{5}$

(Divide by 5 on both sides)

  $\Rightarrow x=48$

(Simplify)

Therefore,

The number of rock songs $=48$

The number of pop songs $=3x$

  $=3\cdot 48$ (Putting the value of x)

  $=144$

The number of hip-hop songs $=32+x$

  $=32+48$ (Putting the value of x)

  $=80$