Patrick purchased some supplies for his guitar students. He bought 25 guitar picks and 35 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.

Answer 1

Let the cost of one guitar pick be \( c \) dollars. According to the problem, the cost of one guitar string is \( c + 1 \) dollars.

Patrick purchased 25 guitar picks and 35 guitar strings. Therefore, the total cost of the guitar picks and strings can be expressed as:

\[ \text{Total cost} = (\text{Number of guitar picks} \times \text{Cost of one guitar pick}) + (\text{Number of guitar strings} \times \text{Cost of one guitar string}) \]

Substituting the values we have:

\[ \text{Total cost} = (25 \times c) + (35 \times (c + 1)) \]

The total cost is given as $40, so we can set up the equation:

\[ 25c + 35(c + 1) = 40 \]

Expanding the expression inside the parentheses gives us:

\[ 25c + 35c + 35 = 40 \]

Combining like terms:

\[ 60c + 35 = 40 \]

Next, we isolate \( c \) by subtracting 35 from both sides:

\[ 60c = 40 - 35 \]

\[ 60c = 5 \]

Now, divide both sides by 60 to solve for \( c \):

\[ c = \frac{5}{60} = \frac{1}{12} \]

Now that we have \( c \), we can determine the cost of one guitar string:

\[ \text{Cost of one guitar string} = c + 1 = \frac{1}{12} + 1 = \frac{1}{12} + \frac{12}{12} = \frac{13}{12} \]

Thus, the cost of one guitar string is:

\[ \boxed{\frac{13}{12}} \text{ dollars} \]

Alternatively, in decimal form, this is approximately $1.08.