Question

this question has two parts. first, answer part a. then, answer part b.
part a
use a model jeremy and kendrick each bought snacks for their friends at a skating rink. the table shows the number of bags of popcorn and the number of plates of nachos each person bought, as well as the total cost of the snacks.

name	bags of popcorn	plates of nachos	total cost
kendrick	7	2	$26.75

a. write a system of equations that you can use to find the prices of the popcorn and the nachos. describe what each variable represents.
let ( p ) be the (\boldsymbol{\text{select choice}}) and let ( n ) be the (\boldsymbol{\text{select choice}}).
part b
(\boldsymbol{\text{select choice}}) ( p + \boldsymbol{\text{select choice}} ) ( n = 18.50 )
(\boldsymbol{\text{select choice}}) ( p + \boldsymbol{\text{select choice}} ) ( n = \boldsymbol{\text{select choice}} )

Explanation:

Part A

Step1: Define variables

Let \( p \) be the price of one bag of popcorn (in dollars), and let \( n \) be the price of one plate of nachos (in dollars).

Step2: Formulate Jeremy's equation

Jeremy bought 4 bags of popcorn and 2 plates of nachos, with a total cost of \$18.50. So the equation is \( 4p + 2n = 18.50 \).

Step3: Formulate Kendrick's equation

Kendrick bought 7 bags of popcorn and 2 plates of nachos, with a total cost of \$26.75. So the equation is \( 7p + 2n = 26.75 \).

Step1: Subtract the two equations

Subtract the first equation (\( 4p + 2n = 18.50 \)) from the second equation (\( 7p + 2n = 26.75 \)) to eliminate \( n \):
\[
(7p + 2n) - (4p + 2n) = 26.75 - 18.50
\]
\[
7p + 2n - 4p - 2n = 8.25
\]
\[
3p = 8.25
\]

Step2: Solve for \( p \)

Divide both sides by 3:
\[
p = \frac{8.25}{3} = 2.75
\]

Step3: Substitute \( p \) into Jeremy's equation

Substitute \( p = 2.75 \) into \( 4p + 2n = 18.50 \):
\[
4(2.75) + 2n = 18.50
\]
\[
11 + 2n = 18.50
\]

Step4: Solve for \( n \)

Subtract 11 from both sides:
\[
2n = 18.50 - 11 = 7.50
\]
Divide both sides by 2:
\[
n = \frac{7.50}{2} = 3.75
\]

Answer:

The system of equations is:
\[

$$\begin{cases} 4p + 2n = 18.50 \\ 7p + 2n = 26.75 \end{cases}$$

\]
where \( p \) is the price (in dollars) of one bag of popcorn and \( n \) is the price (in dollars) of one plate of nachos.

Part B