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

Question

is the cost of one guitar pick, find the cost of one guitar string.

Answer 1

Let \( c \) be the cost of one guitar pick in dollars. Since the guitar strings cost $1 more than the guitar picks, we can express the cost of one guitar string as:

\[ c + 1 \]

Now, since Patrick bought 25 guitar picks and 25 guitar strings, we can set up the equation for the total cost:

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

Simplifying the equation:

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

Combine like terms:

\[ 50c + 25 = 40 \]

Subtract 25 from both sides:

\[ 50c = 15 \]

Now, divide both sides by 50:

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

Thus, the cost of one guitar pick is \( 0.3 \) dollars. Now, we can find the cost of one guitar string:

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

Therefore, the cost of one guitar string is:

\[ \boxed{1.3} \]