To solve the problem, we will first find the ratio of the show's length to the commercial time in a normal episode.
In a normal episode:
- Total length of the episode = 30 minutes
- Commercial time = 8 minutes
The ratio of the show's length to the amount of commercial time in a normal episode is: \[ \text{Ratio} = \frac{\text{Show Length}}{\text{Commercial Time}} = \frac{30}{8} = \frac{15}{4} \]
Now, we know that the season finale will be 90 minutes long, and we want to find out how many minutes of commercials will be included while maintaining the same ratio of show length to commercial time.
Let \( x \) be the amount of commercial time during the finale. The total length of the show including commercials will then be \( 90 + x \) minutes.
Keeping the same ratio, we can set up the equation: \[ \frac{90}{x} = \frac{15}{4} \]
To solve for \( x \), we can cross-multiply: \[ 90 \cdot 4 = 15 \cdot x \] \[ 360 = 15x \]
Now, dividing both sides by 15 gives: \[ x = \frac{360}{15} = 24 \]
Thus, the amount of commercial time during tonight's show will be 24 minutes.
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