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

Question

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 \(\boxed{1.30}\).