Patrick purchased some supplies for his guitar students. He bought 25 guitar pics and 25 guitar strings since they only cost one dollar more than the guitar pics he spent $40 if he is the cost of one guitar pick find the cost of one guitar string.
Let's assume the cost of one guitar pick is "x" dollars.
According to the given information, Patrick bought 25 guitar picks and 25 guitar strings for a total cost of $40.
The cost of 25 guitar picks is 25 * x = 25x dollars.
The cost of 25 guitar strings is (25x + 1) dollars. (since the guitar strings cost one dollar more than the guitar picks)
So we can set up the equation: 25x + 25x + 1 = 40
Combining like terms, we get: 50x + 1 = 40
Subtracting 1 from both sides of the equation: 50x = 40 - 1
Simplifying, we get: 50x = 39
Dividing both sides of the equation by 50, we get: x = 39/50
Therefore, the cost of one guitar pick is $0.78 (rounded to two decimal places).
Since the cost of one guitar string is one dollar more than the guitar pick, the cost of one guitar string is $0.78 + $1 = $1.78. Answer: \boxed{1.78}.