Answer
The number of packages are: $5$ (6 blades), $3$ (12 blades), $4$ (24 blades)
Work Step by Step
Step 1. Assume the number of packages are: $x$ (6 blades), $y$ (12 blades), $z$ (24 blades)
Step 2. Based on the given conditions, we have
$\begin{cases} x+y+z=12\\ 6x+12y+24z=162 \\ 2x+3y+4z=35 \end{cases}$
Step 3. The second equation can be simplified to $x+2y+4z=27$
Step 4. Eliminate $x$ using equations 1-2 and 1-3; we have
$\begin{cases} y+3z=15\\ y+2z=11 \end{cases}$
Step 5. Taking the difference, we have $z=4$; thus $y=3$ and $x=5$
Step 6. We conclude the number of packages are:
$5$ (6 blades), $3$ (12 blades), $4$ (24 blades),
