Question

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 the cost of one guitar pick be \( c \) dollars. Given that the cost of one guitar string is \( c + 1 \) dollars, Patrick bought 25 of each.

The total cost for the guitar picks is: \[ 25c \]

The total cost for the guitar strings is: \[ 25(c + 1) = 25c + 25 \]

The total amount he spent is the sum of both costs, which is given as $40: \[ 25c + (25c + 25) = 40 \]

Combining the terms, we get: \[ 50c + 25 = 40 \]

Now, we will solve for \( c \): \[ 50c = 40 - 25 \] \[ 50c = 15 \] \[ c = \frac{15}{50} = \frac{3}{10} = 0.30 \]

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

Now, we can find the cost of one guitar string: \[ c + 1 = 0.30 + 1 = 1.30 \]

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