Question

An airplane has a total of 414 packets of crackers, pretzels, and peanuts available for passengers.

Answer 1

There is no question in Part A, but i do what i can.

Part A.
We know that:

n - number of packets of crackers
p - number of packets of pretzels

p = 2n+9

s - number of packets of peanuts

s = 3p = 3(2n+9) = 6n+27

So:

$n+p+s=414\\\\n+(2n+9)+(6n+27)=414\\\\9n+36=414\quad|-36\\\\9n=378\quad|:9\\\\\boxed{n=42}\\\\\\ p=2n+9=2\cdot42+9=\boxed{93}\\\\s=6n+27=6\cdot42+27=\boxed{279}$

There are 42 packets of crackers, 93 packets of pretzels and 279 packets of peanuts.

Part B.

x - number of rows with exactly 2 passengers
y - number of rows with exactly 3 passengers

and:

$\boxed{\begin{cases}x+y=48\\2x+3y=132\end{cases}}\\\\\\ \begin{cases}x+y=48\quad|\cdot2\\2x+3y=132\end{cases}\\\\\\ \begin{cases}2x+2y=96\\2x+3y=132\end{cases}\\\\--------(-)\\\\2x-2x+2y-3y=96-132\\\\-y=-36\\\\\boxed{y=36}\\\\\\x+y=48\\\\x+36=48\\\\x=48-36\\\\\boxed{x=12}$

There are 12 rows with exactly 2 passengers and 36 rows with exactly 3 passengers.