I bought 25 guitar picks and 25 strings.. Strings cost $1 more than picks. I spent $50 on both. Find the cost of one guitar string?

Answer 1

Let the cost of one guitar pick be \( p \) dollars. Then the cost of one guitar string would be \( p + 1 \) dollars.

You bought 25 guitar picks and 25 guitar strings. The total cost can be expressed as:

\[ 25p + 25(p + 1) = 50 \]

Now, simplifying the equation:

\[ 25p + 25p + 25 = 50 \]

Combine the terms:

\[ 50p + 25 = 50 \]

Now, subtract 25 from both sides:

\[ 50p = 25 \]

Dividing both sides by 50 gives:

\[ p = \frac{25}{50} = \frac{1}{2} \]

So, the cost of one guitar pick is \( \frac{1}{2} \) dollar or 50 cents.

Now, to find the cost of one guitar string:

\[ p + 1 = \frac{1}{2} + 1 = \frac{1}{2} + \frac{2}{2} = \frac{3}{2} \]

The cost of one guitar string is therefore:

\[ \frac{3}{2} \text{ dollars} = 1.50 \text{ dollars} \]

Thus, the cost of one guitar string is $1.50.