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. Kenny wants to solve for the number of each type of string, so he represents variables as shown.

Let x = the number of premium strings.

Let y = the number of standard strings.

The equation for the total number of strings ordered is
.
The equation based on the price of each type of string and the total value of the order is
.

Answer 1

To solve for the number of each type of guitar string Kenny ordered, we can set up two equations based on the information provided.

1. The total number of strings ordered:
\[
x + y = 80
\]

Here, \( x \) represents the number of premium strings and \( y \) represents the number of standard strings.

2. The total value of the order based on the prices:
\[
4.50x + 1.50y = 225
\]

Now, we have a system of linear equations:

1. \( x + y = 80 \)
2. \( 4.50x + 1.50y = 225 \)

With these equations, Kenny can now solve for \( x \) and \( y \).