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

Answer 1

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

Patrick bought 25 guitar picks and 25 guitar strings. Therefore, we can express the total cost as follows:

\[
\text{Total cost} = (\text{Cost of guitar picks}) + (\text{Cost of guitar strings})
\]
\[
= 25c + 25(c + 1)
\]
\[
= 25c + 25c + 25
\]
\[
= 50c + 25
\]

According to the problem statement, the total cost was $40. Therefore, we set up the equation:

\[
50c + 25 = 40
\]

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

\[
50c = 40 - 25
\]
\[
50c = 15
\]

Next, we divide both sides 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:

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

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