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.(1 point)
$__

Answer 1

Let \( c \) be the cost of one guitar pick. Since the guitar strings cost $1 more than the guitar picks, the cost of one guitar string would be \( c + 1 \).

Patrick bought 25 guitar picks and 25 guitar strings. Therefore, the total cost can be represented as:

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

Now, we can simplify the equation:

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

This simplifies to:

\[ 50c + 25 = 40 \]

Next, subtract 25 from both sides:

\[ 50c = 15 \]

Now, divide by 50:

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

Now that we know the cost of one guitar pick is \( 0.30 \), we can 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:

\[ \boxed{1.30} \]