Question

Patrick purchased some supplies for his guitar students.He bought 25 guitar picks and 25 guitar strings.Since they only cost a dollar 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 the cost of one guitar pick be \( c \) dollars.

Given that the cost of one guitar string is \( c + 1 \) dollars (since the guitar strings cost a dollar more than the guitar picks), we can set up the total cost equation based on the quantities purchased:

- He purchased 25 guitar picks at \( c \) dollars each.
- He purchased 25 guitar strings at \( c + 1 \) dollars each.

The total cost can be expressed as:

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

Expanding the equation:

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

Combine like terms:

\[
50c + 25 = 40
\]

Now, subtract 25 from both sides:

\[
50c = 15
\]

Next, divide both sides by 50:

\[
c = \frac{15}{50} = \frac{3}{10} = 0.3
\]

So the cost of one guitar pick is \( \$0.30 \).

Now, we can find the cost of one guitar string:

\[
c + 1 = 0.3 + 1 = 1.3
\]

Thus, the cost of one guitar string is \( \$1.30 \).

Therefore, the final answer is:

\[
\boxed{1.30}
\]