Let the cost of one guitar pick be \( p \) dollars. Since the strings cost $1 more than the picks, the cost of one guitar string will be \( p + 1 \) dollars.
You bought 25 guitar picks and 25 strings, so the total cost can be expressed as:
\[ 25p + 25(p + 1) = 50 \]
Now, let's simplify this equation:
\[ 25p + 25(p + 1) = 25p + 25p + 25 = 50 \] \[ 50p + 25 = 50 \]
Next, subtract 25 from both sides:
\[ 50p = 25 \]
Now, divide by 50:
\[ p = \frac{25}{50} = 0.5 \]
So, the cost of one guitar pick is \( 0.5 \) dollars. Now, to find the cost of one guitar string:
\[ \text{Cost of one string} = p + 1 = 0.5 + 1 = 1.5 \]
Thus, the cost of one guitar string is \( \boxed{1.5} \) dollars.