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 one guitar pick, find the cost of one guitar string.(1 point) $

Answer 1

Let the cost of one guitar pick be \( c \). Since the guitar strings cost $1 more than the guitar picks, the cost of one guitar string will be \( c + 1 \).

Patrick bought 25 guitar picks and 25 guitar strings, so the total cost can be expressed as:

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

This simplifies to:

\[
25c + 25c + 25 = 50c + 25
\]

According to the problem, the total amount spent is $40, so we can set up the equation:

\[
50c + 25 = 40
\]

To solve for \( c \), first, subtract 25 from both sides:

\[
50c = 15
\]

Next, divide by 50:

\[
c = \frac{15}{50} = \frac{3}{10} = 0.30
\]

Now that we have the cost of one guitar pick, we can find the cost of one guitar string:

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

Thus, the cost of one guitar string is:

\[
\boxed{1.30}
\]