Question

1. jared wants to have his birthday party at the movies. the special event price of a movie ticket is $8 per person plus $4 per person for popcorn and a drink. the cost to rent the party room after the movie is $50 plus $5 per person for pop and cake.

a) write an expression to represent the cost of a ticket with popcorn and a drink.
b) write an expression to represent the cost of renting the party room and having pop and cake.
c) what is the simplified expression for the total cost of jared’s birthday party?
d) how much would it cost for jared’s birthday at the movies, including the party room, for jared and five friends?

Explanation:

Part (a)

Step 1: Define the variable

Let \( n \) be the number of people. The cost of a movie ticket is \(\$8\) per person and the cost for popcorn and a drink is \(\$4\) per person.

Step 2: Write the expression

To find the cost of a ticket with popcorn and a drink, we add the cost of the ticket and the cost of popcorn and a drink for each person. So the expression is \( 8n + 4n \). We can simplify this by combining like terms: \( (8 + 4)n=12n \).

Part (b)

Step 1: Define the variable

Let \( n \) be the number of people. The cost to rent the party room is a fixed cost of \(\$50\) and the cost for pop and cake is \(\$5\) per person.

Step 2: Write the expression

The cost of renting the party room and having pop and cake is the fixed cost plus the cost per person for pop and cake. So the expression is \( 50+5n \).

Part (c)

Step 1: Recall the expressions from (a) and (b)

From part (a), the cost of the ticket with popcorn and drink is \( 12n \). From part (b), the cost of the party room and pop and cake is \( 50 + 5n \).

Step 2: Find the total cost expression

To find the total cost, we add the two expressions together: \( 12n+(50 + 5n) \).

Step 3: Simplify the expression

Combine like terms: \( 12n+5n + 50=(12 + 5)n+50 = 17n+50 \).

Part (d)

Step 1: Determine the number of people

Jared and five friends, so the number of people \( n=1 + 5=6 \).

Step 2: Substitute \( n = 6 \) into the total cost expression

The total cost expression from part (c) is \( 17n+50 \). Substitute \( n = 6 \): \( 17\times6+50 \).

Step 3: Calculate the value

First, calculate \( 17\times6 = 102 \). Then add \( 50 \): \( 102+50 = 152 \).

Answer:

s:
a) \(\boldsymbol{12n}\) (or \(8n + 4n\))
b) \(\boldsymbol{50 + 5n}\)
c) \(\boldsymbol{17n+50}\)
d) \(\boldsymbol{\$152}\)