The weekly cost of running a small firm is a function of the number of employees. Every week there is a fixed cost of $3000, and each employee costs the firm $300. For example, if there are 10 employees, then the weekly cost is 3000 + 300 × 10 = 6000 dollars.
(a) What is the weekly cost if there are 5 employees?
$ 4500


(b) Find a formula for the weekly cost C as a function of the number of employees n.
C = 
 


Let's break this down step by step:

### (a) What is the weekly cost if there are 5 employees?

The fixed cost is $3000, and each employee costs $300 per week. For 5 employees:

\[
\text{Weekly Cost} = 3000 + 300 \times 5 = 3000 + 1500 = 4500 \text{ dollars}
\]

So, the weekly cost for 5 employees is **$4500**.

### (b) Find a formula for the weekly cost $ C $ as a function of the number of employees $ n $.

We are given:
- A fixed cost of $3000.
- Each employee costs $300.

Thus, the weekly cost $ C $ is a linear function of the number of employees $ n $, and can be expressed as:

\[
C(n) = 3000 + 300n
\]

### Summary:
- (a) The weekly cost for 5 employees is **$4500**.
- (b) The formula for the weekly cost is $ C(n) = 3000 + 300n $, where $ n $ is the number of employees.

Would you like more details, or have any questions?

Here are five related questions to expand on this concept:
1. What is the weekly cost for 15 employees?
2. If the weekly cost is $5400, how many employees does the firm have?
3. What happens to the weekly cost if the cost per employee increases to $350?
4. How would you modify the formula if there is an additional variable cost per employee?
5. How does the weekly cost change if the fixed cost increases by $500?

**Tip:** When solving word problems, clearly identify fixed and variable components to create an accurate mathematical model.

The weekly cost of running a small firm is a function of the number of employees. Every week there is a fixed cost of $3000, and each employee costs the firm $300. For example, if there are 10 employees, then the weekly cost is 3000 + 300 × 10 = 6000 dollars.
(a) What is the weekly cost if there are 5 employees?
(b) Find a formula for the weekly cost C as a function of the number of employees n.

This page explores how to calculate the weekly costs of running a small firm. With a fixed cost of $3000 and a variable employee cost of $300 per person, find the total cost for any number of employees. Includes formula derivation and example calculations. Suitable for Grades 6-8.

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