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.

Question

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.