Question

Patrick purchased some supplies for his guitar students He bought 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 1 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 a guitar string is \( c + 1 \).

Patrick purchased 25 guitar picks and 25 guitar strings. Therefore, the total cost can be expressed as follows:

\[
\text{Total cost} = (25 \text{ guitar picks}) \times c + (25 \text{ guitar strings}) \times (c + 1)
\]

This can be simplified to:

\[
\text{Total cost} = 25c + 25(c + 1)
\]

Let's further simplify:

\[
\text{Total cost} = 25c + 25c + 25 = 50c + 25
\]

According to the problem, he spent a total of $40, hence we set up the equation:

\[
50c + 25 = 40
\]

Now, let's solve for \( c \):

1. Subtract 25 from both sides:
\[
50c = 40 - 25
\]
\[
50c = 15
\]

2. Divide both sides by 50:
\[
c = \frac{15}{50} = \frac{3}{10} = 0.30
\]

Thus, the cost of one guitar pick is \( $0.30 \).

Now, to find the cost of one guitar string:

\[
\text{Cost of one guitar string} = c + 1 = 0.30 + 1 = 1.30
\]

Therefore, the cost of one guitar string is

\[
\boxed{1.30}
\]