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

Answer 1

Let's denote the cost of one guitar pick as \( c \). According to the problem, the cost of one guitar string is \( c + 1 \).

Patrick bought:
- 25 guitar picks
- 25 guitar strings

The total cost for the guitar picks is \( 25c \). The total cost for the guitar strings is \( 25(c + 1) \).

The total amount Patrick spent is $40:

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

Now, simplify the equation:

\[
25c + 25c + 25 = 40
\]
\[
50c + 25 = 40
\]

Next, subtract 25 from both sides:

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

Now, divide by 50:

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

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

Now, we need to 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 \( \boxed{1.30} \).