Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 25 guitar strings since they only cost $1.00 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?

Answer 1

Let's denote the cost of one guitar pick as \( c \). According to the problem, the cost of one guitar string is \( c + 1 \).

Patrick bought 25 guitar picks and 25 guitar strings, and we can set up the following equation for the total cost:

\[ 25c + 25(c + 1) = 40 \]

Now, let's simplify this equation:

1. Distribute the \( 25 \) on the second term: \[ 25c + 25c + 25 = 40 \]

2. Combine like terms: \[ 50c + 25 = 40 \]

3. Subtract \( 25 \) from both sides: \[ 50c = 15 \]

4. Divide by \( 50 \): \[ c = \frac{15}{50} = \frac{3}{10} = 0.30 \]

So, the cost of one guitar pick is \( 0.30 \) dollars. Now, we can find the cost of one guitar string:

\[ c + 1 = 0.30 + 1 = 1.30 \]

Thus, the cost of one guitar string is \(\boxed{1.30}\) dollars.