Let \( x \) represent the distance Triana will travel each of the remaining three days. After traveling 24 miles on the first day, the total distance she has left to cover is:
\[ 120 - 24 = 96 \text{ miles} \]
Since she wants to travel equal distances over the remaining three days, we can express this as:
\[ 3x = 96 \]
To write this in the form \( px + q = r \), we can rearrange it as follows:
\[ 3x + 0 = 96 \]
In this equation, \( p = 3 \), \( q = 0 \), and \( r = 96 \).
Now, to solve for \( x \):
\[ 3x = 96 \] \[ x = \frac{96}{3} = 32 \]
Thus, Triana will travel 32 miles on each of the remaining three days.
In conclusion, after completing the first day of her 120-mile bike ride by traveling 24 miles, Triana has 96 miles left to travel over the next three days. To ensure she travels an equal distance each day, we set up the equation \( 3x = 96 \), where \( x \) represents the distance she will travel each day. Solving this equation, we find that she will travel 32 miles each day for the next three days, which balances her total ride to 120 miles.