Math / Algebra

QuestionA student agrees to throw a party, provided that each guest shares the expenses equally with him. A four-person local band will play for $\$ 200$ and free drinks and snacks. The student estimates that the mean cost of drinks and snacks will be $\$ 2$ per person. a. Suppose that $n$ people (including the host and band members) attend the party. Let $C(n)$ be the party's total cost (in dollars). Find an equation of $C$ . $C(n)=$ $\square$ (Do not factor.)

Studdy Solution

STEP 1

What is this asking? We need to find the total cost of the party, considering the band's fee and the cost of snacks and drinks per person. Watch out! Don't forget to include the band members in the total number of people at the party when calculating the snack and drink costs!

STEP 2

1. Define the function
2. Calculate the result

STEP 3

Alright, let's define our cost function $C(n)$ !
Remember, $n$ is the total number of people at the party, including our awesome student host and the rocking band members.

STEP 4

The band's fee is a fixed cost of $\$200$ , no matter how many people show up.
So, that's our starting point.

STEP 5

Next, we've got the variable cost of snacks and drinks.
It's $\$2$ per person, and since there are $n$ people, the total cost for snacks and drinks is $2 \cdot n$ .

STEP 6

To get the total cost, we just add the fixed cost and the variable cost together.
So, our function is $C(n) = 200 + 2 \cdot n$ .
Boom!

STEP 7

We've already calculated our function in the previous step!
We found that the total cost of the party, given $n$ attendees, is given by $C(n) = 200 + 2 \cdot n$ .

STEP 8

$C(n) = 200 + 2n$

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Studdy Solution

STEP 1

What is this asking? We need to find the total cost of the party, considering the band's fee and the cost of snacks and drinks per person. Watch out! Don't forget to include the band members in the total number of people at the party when calculating the snack and drink costs!

STEP 2

1. Define the function
2. Calculate the result

STEP 3

Alright, let's define our cost function $C(n)$ !
Remember, $n$ is the total number of people at the party, including our awesome student host and the rocking band members.

STEP 4

The band's fee is a fixed cost of $\$200$ , no matter how many people show up.
So, that's our starting point.

STEP 5

Next, we've got the variable cost of snacks and drinks.
It's $\$2$ per person, and since there are $n$ people, the total cost for snacks and drinks is $2 \cdot n$ .

STEP 6

To get the total cost, we just add the fixed cost and the variable cost together.
So, our function is $C(n) = 200 + 2 \cdot n$ .
Boom!

STEP 7

We've already calculated our function in the previous step!
We found that the total cost of the party, given $n$ attendees, is given by $C(n) = 200 + 2 \cdot n$ .

STEP 8

$C(n) = 200 + 2n$

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Studdy Solution

STEP 1

What is this asking? We need to find the total cost of the party, considering the band's fee and the cost of snacks and drinks per person. Watch out! Don't forget to include the band members in the total number of people at the party when calculating the snack and drink costs!

STEP 2

1. Define the function2. Calculate the result

STEP 3

Alright, let's **define** our cost function C(n)C(n)C(n)!Remember, nnn is the **total number of people** at the party, including our awesome student host *and* the rocking band members.

STEP 4

The band's fee is a **fixed cost** of $200\$200$200, no matter how many people show up.So, that's our starting point.

STEP 5

Next, we've got the **variable cost** of snacks and drinks.It's $2\$2$2 per person, and since there are nnn people, the total cost for snacks and drinks is 2⋅n2 \cdot n2⋅n.

STEP 6

To get the **total cost**, we just **add** the fixed cost and the variable cost together.So, our function is C(n)=200+2⋅nC(n) = 200 + 2 \cdot nC(n)=200+2⋅n.Boom!

STEP 7

We've already **calculated** our function in the previous step!We found that the total cost of the party, given nnn attendees, is given by C(n)=200+2⋅nC(n) = 200 + 2 \cdot nC(n)=200+2⋅n.

STEP 8

C(n)=200+2nC(n) = 200 + 2nC(n)=200+2n

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Define the function
2. Calculate the result

Alright, let's define our cost function $C(n)$ !
Remember, $n$ is the total number of people at the party, including our awesome student host and the rocking band members.

The band's fee is a fixed cost of $\$200$ , no matter how many people show up.
So, that's our starting point.

Next, we've got the variable cost of snacks and drinks.
It's $\$2$ per person, and since there are $n$ people, the total cost for snacks and drinks is $2 \cdot n$ .

To get the total cost, we just add the fixed cost and the variable cost together.
So, our function is $C(n) = 200 + 2 \cdot n$ .
Boom!

We've already calculated our function in the previous step!
We found that the total cost of the party, given $n$ attendees, is given by $C(n) = 200 + 2 \cdot n$ .

$C(n) = 200 + 2n$