Alright, let's tackle this step by step.
### Step 1: Define the Variables
First, let's define our variables:
- [tex]\( x \)[/tex] represents the number of packages of 6 razor blades.
- [tex]\( y \)[/tex] represents the number of packages of 12 razor blades.
- [tex]\( z \)[/tex] represents the number of packages of 24 razor blades.
### Step 2: Write the Equations
Based on the problem description, we can create the following system of linear equations:
1. The total number of razor blades sold:
[tex]\[ 6x + 12y + 24z = 234 \][/tex]
2. The total revenue from the sales:
[tex]\[ 2x + 3y + 4z = 50 \][/tex]
3. The total number of packages sold:
[tex]\[ x + y + z = 17 \][/tex]
Therefore, the correct system of linear equations is:
[tex]\[
\left\{
\begin{array}{l}
6x + 12y + 24z = 234 \\
2x + 3y + 4z = 50 \\
x + y + z = 17 \\
\end{array}
\right.
\][/tex]
### Step 3: Solve the System of Equations
Let's solve this system of equations. The calculated solution shows that:
[tex]\[ x = 7 \][/tex]
[tex]\[ y = 4 \][/tex]
[tex]\[ z = 6 \][/tex]
### Step 4: Interpret the Solution
Thus, the store sold:
- [tex]\( 7 \)[/tex] packages of 6 razor blades,
- [tex]\( 4 \)[/tex] packages of 12 razor blades,
- [tex]\( 6 \)[/tex] packages of 24 razor blades.
#### Final Answer:
There were [tex]\(\boxed{7}\)[/tex] packages of 6 blades, [tex]\(\boxed{4}\)[/tex] packages of 12 blades, and [tex]\(\boxed{6}\)[/tex] packages of 24 blades sold.
