Carter purchased some supplies for his gitar students. He bought 32 guitar picks *

Question

and 32 guitar strings since they only cost $1 more than the guitar picks. He spent

a total of $48. If c is the cost of one guitar pick, find the cost of one guitar string.
© $1.32

© $1.25

© $1.75

© $1.50

Answer 1

Let the cost of one guitar pick be \( c \). The cost of one guitar string, then, is \( c + 1 \) (since it costs $1 more than the guitar pick).

Carter bought 32 guitar picks and 32 guitar strings. The total cost can be represented as:

\[ 32c + 32(c + 1) = 48 \]

Expanding this, we get:

\[ 32c + 32c + 32 = 48 \]

Combining like terms results in:

\[ 64c + 32 = 48 \]

Next, we subtract 32 from both sides:

\[ 64c = 48 - 32 \] \[ 64c = 16 \]

Now, we divide both sides by 64 to solve for \( c \):

\[ c = \frac{16}{64} = \frac{1}{4} = 0.25 \]

So, the cost of one guitar pick is $0.25. Therefore, the cost of one guitar string is:

\[ c + 1 = 0.25 + 1 = 1.25 \]

Thus, the cost of one guitar string is $1.25.

The answer is:

© $1.25