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 \( c \) be the cost of one guitar pick. Since the cost of one guitar string is \( c + 1 \), we can set up the equation based on the total cost for purchasing 25 guitar picks and 25 guitar strings.

The total cost can be expressed as:

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

Now, let's simplify the equation:

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

Combining like terms:

\[
50c + 25 = 40
\]

Next, subtract 25 from both sides:

\[
50c = 15
\]

Now, 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:

\[
c + 1 = 0.30 + 1 = 1.30
\]

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