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

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

Now, let's simplify this equation:

\[
25c + 25c + 25 = 40
\]

Combining like terms gives:

\[
50c + 25 = 40
\]

Subtracting 25 from both sides:

\[
50c = 15
\]

Dividing both sides by 50:

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

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

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 \(\boxed{1.30}\).