Question

Kenny ordered guitar strings for Glenn’s Guitar Shop. The premium guitar strings are $4.50 apiece. The standard guitar strings are $1.50 apiece. The bill smeared in the rain, but Kenny knows he ordered a total of 80 strings for $225.

Let x = the number of premium strings.

Let y = the number of standard strings.

x + y = 80,

4.50x + 1.50y = 225

How many of each type of string did Kenny order?

He ordered
premium strings.
He ordered
standard strings.

Answer 1

We can solve the problem by using the two equations provided.

1. From the first equation, we have:

\[
x + y = 80
\]

2. From the second equation, we have:

\[
4.50x + 1.50y = 225
\]

To solve this system of equations, we can first express \( y \) in terms of \( x \) using the first equation:

\[
y = 80 - x
\]

Now, we can substitute \( y \) in the second equation:

\[
4.50x + 1.50(80 - x) = 225
\]

Distributing \( 1.50 \):

\[
4.50x + 120 - 1.50x = 225
\]

Combining like terms:

\[
(4.50 - 1.50)x + 120 = 225
\]
\[
3x + 120 = 225
\]

Now, subtract 120 from both sides:

\[
3x = 225 - 120
\]
\[
3x = 105
\]

Now, divide by 3:

\[
x = 35
\]

Now that we have \( x \), we can find \( y \):

\[
y = 80 - x = 80 - 35 = 45
\]

So, Kenny ordered:

- **35 premium guitar strings.**
- **45 standard guitar strings.**

Thus:

He ordered 35 premium strings.
He ordered 45 standard strings.