Chapter 6.4, Problem 6CYU

To determine

To find the number of podcasts in each tag that Steve subscribed.

Answer to Problem 6CYU

Hobbies and Recreation: 8 podcasts

Soliloquies: 2 podcasts

Explanation of Solution

Given:

Steve subscribed to 10 podcasts for 340 minutes.

Duration of Hobbies and Recreation each episode: 32 minutes

Duration of Soliloquies each episode: 42 minutes.

Calculation:

Let x be the number of episodes in Hobbies and Recreation and y be the number of episodes in Soliloquies.

Total number of podcasts subscribed is

  $x+y=\mathrm{10.................................}(1)$

Duration of the podcasts is

  $32x+42y=\mathrm{340.......................}(2)$

Multiplying equation (1) with 32,

  $32x+32y=\mathrm{320.................................}(3)$

Subtract equation (3) from equation (1),

  $\begin{array}{l}\Rightarrow (32x+42y)-(32x+32y)=340-320\\ \Rightarrow 32x+42y-32x-32y=20\\ \Rightarrow 10y=20\\ \Rightarrow y=2\end{array}$

Substitute the value of y in equation (1),

  $\begin{array}{l}\Rightarrow x+2=10\\ \Rightarrow x=10-2\\ \Rightarrow x=8\end{array}$

Conclusion:

Therefore, Steve has subscribed to 8 podcasts in Hobbies and Recreation and 2 podcasts in Soliloquies.