Question

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's denote the cost of one guitar pick as \( p \) and the cost of one guitar string as \( s \). According to the problem, we have the following information:

1. You bought 25 guitar picks and 25 guitar strings.
2. The cost of guitar strings is $1 more than the cost of guitar picks, which gives us the equation:
\[
s = p + 1
\]
3. You spent a total of $50 on both picks and strings. This gives us the equation:
\[
25p + 25s = 50
\]

Now, let's simplify the second equation by dividing everything by 25:
\[
p + s = 2
\]

Now we have a system of equations:
1. \( s = p + 1 \)
2. \( p + s = 2 \)

Next, we can substitute the first equation into the second:
\[
p + (p + 1) = 2
\]
\[
2p + 1 = 2
\]
Subtract 1 from both sides:
\[
2p = 1
\]
Now, divide by 2:
\[
p = 0.5
\]

Now that we have the cost of one guitar pick, we can find the cost of one guitar string:
\[
s = p + 1 = 0.5 + 1 = 1.5
\]

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