Let's denote the cost of one guitar pick as \( p \) and the cost of one guitar string as \( s \). According to the problem, we have the following information:
- You bought 25 guitar picks and 25 guitar strings.
- The cost of guitar strings is $1 more than the cost of guitar picks, which gives us the equation: \[ s = p + 1 \]
- You spent a total of $50 on both picks and strings. This gives us the equation: \[ 25p + 25s = 50 \]
Now, let's simplify the second equation by dividing everything by 25: \[ p + s = 2 \]
Now we have a system of equations:
- \( s = p + 1 \)
- \( p + s = 2 \)
Next, we can substitute the first equation into the second: \[ p + (p + 1) = 2 \] \[ 2p + 1 = 2 \] Subtract 1 from both sides: \[ 2p = 1 \] Now, divide by 2: \[ p = 0.5 \]
Now that we have the cost of one guitar pick, we can find the cost of one guitar string: \[ s = p + 1 = 0.5 + 1 = 1.5 \]
Thus, the cost of one guitar string is $1.50.