Question

Patrick purchased some supplies for his guitar students. He bought 25 guitar strings since they 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 \( c \) represent the cost of one guitar pick. 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 strings, and he spent a total of $40 on guitar strings and picks. We can set up the following equation based on the total cost he spent:

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

Here, \( x \) is the number of guitar picks purchased. We know that \( 25(c + 1) \) represents the total cost of the guitar strings, and \( x \cdot c \) represents the total cost of the guitar picks.

Since the problem doesn’t specify the number of picks, we'll assume he purchased none for simplicity (since only the strings cost is mentioned), leading to:

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

Now we simplify and solve this equation:

\[
25c + 25 = 40
\]

Subtract 25 from both sides:

\[
25c = 15
\]

Now, divide both sides by 25:

\[
c = \frac{15}{25} = \frac{3}{5} = 0.6
\]

Thus, the cost of one guitar pick is $0.60. To find the cost of one guitar string:

\[
\text{Cost of one guitar string} = c + 1 = 0.6 + 1 = 1.6
\]

So, the cost of one guitar string is **$1.60**.