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

There are n packets of crackers.
There number of packets of pretzels is 9 more than twice the number of packets of crackers.
The number of packets of peanut is 3 times the number of packets of pretzels.

Part B

The airplane has seats for 144 passengers. The seats are arranged in 48 rows, with 3 seats in each row.

There are 132 passengers on a certain flight.
There are exactly 2 passengers in x rows.
There are exactly 3 passengers in y rows.

Write a system of linear equations that can be used to model the situation. Use your system to determine the number of rows with exactly 2 passengers and the number of rows with exactly 3 passengers. Show your work.

Question

02-09-2017
Mathematics

contestada

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

There are n packets of crackers.
There number of packets of pretzels is 9 more than twice the number of packets of crackers.
The number of packets of peanut is 3 times the number of packets of pretzels.

Part B

The airplane has seats for 144 passengers. The seats are arranged in 48 rows, with 3 seats in each row.

There are 132 passengers on a certain flight.
There are exactly 2 passengers in x rows.
There are exactly 3 passengers in y rows.

Write a system of linear equations that can be used to model the situation. Use your system to determine the number of rows with exactly 2 passengers and the number of rows with exactly 3 passengers. Show your work.

Respuesta :

Otras preguntas

A good is non-rival in consumption if ________. one person's use of the good does not preclude consumption by others the government can regulate its production

Where is primary succession likely to occur? in a field that has recently been mowed O near the base of a mature shade tree O at the deepest point on the ocean

In an automobile parts factory, for every 175 carburetors 3 are found to be defective. At that rate how many carbureatots out of 1,050 could be expective to be

El libro de vida contesta estas preguntas

John owes $829.30 to discover card. However his payment of $35 is late resulting in a late fee of $35. If his new balance $847.96, what is the annual interest r

/* * Write a method called showTwos that shows the factors of 2 in a given integer. * For example, consider the following calls: showTwos(7); showTwos(18);

Stanford owns and operates two dry cleaning businesses. He travels to Boston to discuss acquiring a restaurant. Later in the month, he travels to New York to di

During an early phase of the planet's existence, Earth's atmosphere was similar in composition to the atmospheres of Mars and Venus. At that time Earth's princi

Which statement is true about reporting receivables on the balance sheet? A) Bad Debts Expense is subtracted from Accounts Receivable and is then shown as a ded

max is a function that accepts two int parameters and returns the value of the larger one. Two int variables, population1 and population2, have already been dec

WojtekR WojtekR · Answer 1 · 2017-09-02T01:29:50+02:00

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:

[tex]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}[/tex]

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:

[tex]\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}[/tex]

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