Patrick purchased some supplies for his guitar students. He brought 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 one guitar pick, find the cost of one guitar string.
$___
If Patrick bought 25 guitar picks and 25 guitar strings, and they cost a total of $40, the total cost of the guitar picks is 25*c = $40 - c.
As the cost of the guitar strings is $1 more than that of the guitar picks, the cost of the guitar strings is c + $1.
Since he bought 25 guitar strings, the total cost of the guitar strings is 25 * (c + $1).
Since the total cost of the guitar picks and the total cost of the guitar strings add up to $40, the equation 25*c + 25 * (c + $1) = $40.
Multiplying 25 by the price of the guitar picks (c), the equation becomes 25c + 25(c + $1) = $40
Simplifying the equation gives 25c + 25c + 25 equal to $40.
Combining like terms, the equation becomes 50c + 25 = $40
To isolate c, subtract 25 from both sides giving 50c = 40 - 25
Subtracting on the right gives 50c = 15.
Dividing both sides by 50 to simplify for c gives c = 15/50
Dividing the numerator by the denominator gives c = 3/10.
The cost of one guitar pick is $0.3 since 3/10 = 0.3.
Since the cost of the guitar strings is a dollar more than the cost of the guitar picks, the cost of a guitar string is $0.3 plus $1, which is $1.3. Answer: \boxed{1.3}.