Question

The daily listening audience of an AM radio station is four times as large as that of its FM sister station. If 105,000 people listen to these two radio stations, how many listeners does the FM station have?

Answer 1

The number of listeners is given from the total number of listeners and

the ratio of the listeners between the two stations.

Required:

• The FM sister station has 21,000 listeners

How is the given ratio of listeners used to find the number of listeners?

Given:

The daily listening audience of the AM station = 4 × The audience of the FM sister station

The number of people that listen to the two stations = 105,000

Required:

The number of listeners of the FM station

Solution:

The ratio of the listeners is 1:4

Let x represent the number of listeners of the FM sister station, we have;

The number of listeners of AM radio station = 4·x

Which gives;

4·x + x = 105,000

5·x = 105,000

$x = \dfrac{105,000}{5} = \mathbf{21,000}$

• The number of listeners of the FM sister station, x = 21,000

The number of listeners of he radio station = 21,000 × 4 = 84,000

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