To find out how many rock songs Fernando has on his road trip playlist while maintaining the same ratio of country songs to rock songs as his summer playlist, we first determine the ratio from the summer playlist.
Fernando's summer playlist has:
- 100 country songs
- 24 rock songs
The ratio of country songs to rock songs on the summer playlist can be expressed as:
\[ \text{Ratio} = \frac{100}{24} \]
To simplify this ratio, we can divide both the numerator and the denominator by 4:
\[ \frac{100 \div 4}{24 \div 4} = \frac{25}{6} \]
This means the ratio of country songs to rock songs is 25:6.
Now for the road trip playlist, we know that Fernando has 25 country songs. Let \( r \) represent the number of rock songs in the road trip playlist. Keeping the same ratio, we can set up the equation:
\[ \frac{25}{r} = \frac{25}{6} \]
To solve for \( r \), we can cross-multiply:
\[ 25 \cdot 6 = 25 \cdot r \] \[ 150 = 25r \]
Now, we divide both sides by 25:
\[ r = \frac{150}{25} = 6 \]
Thus, the number of rock songs on Fernando's road trip playlist is:
\[ \boxed{6} \]
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