Let the cost of one guitar pick be \( p \) dollars. Then, the cost of one guitar string would be \( p + 1 \) dollars (since the string costs $1 more than a pick).
You bought 25 picks and 25 strings, and the total cost is $50. We can set up the following equation based on the total cost:
\[ 25p + 25(p + 1) = 50 \]
Expanding this equation:
\[ 25p + 25p + 25 = 50 \]
Combining like terms:
\[ 50p + 25 = 50 \]
Now, subtract 25 from both sides:
\[ 50p = 25 \]
Now, divide both sides by 50:
\[ p = \frac{25}{50} = \frac{1}{2} \]
So, the cost of one guitar pick is \( \frac{1}{2} \) dollars. Therefore, the cost of one guitar string, which is \( p + 1 \), is:
\[ \frac{1}{2} + 1 = \frac{1}{2} + \frac{2}{2} = \frac{3}{2} = 1.5 \]
Thus, the cost of one guitar string is $1.50.
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