Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1 more than the guitar picks. He spent a total of $40. If c is the cost of 1 guitar pick, find the cost of one guitar string.
Let the cost of 1 guitar string be s.
The cost of 1 guitar pick is c = s - 1.
Patrick bought 25 guitar picks for a total cost of 25 * c = 25 * (s - 1).
He bought 25 guitar strings for a total cost of 25 * s.
The total cost of the purchases is 25 * (s - 1) + 25 * s = $40.
This simplifies to 50 * s - 25 = $40.
Adding 25 to both sides gives 50 * s = $65.
Dividing both sides by 50 gives s = $65 / 50 = $<<65/50=1.30>>1.30.
The cost of one guitar string is $1.30. Answer: \boxed{1.30}.