Linear Functions & Models

Question

Kara's Custom Tees experienced fixed costs of ​$500 and variable costs of ​$5 a shirt. Write an equation that can be used to determine the total expenses encountered by​ Kara's Custom Tees. Let x be the number of​ shirts, and let​ C(x) be the total cost of producing x shirts.​ Then, calculate the cost of producing 7 shirts.

Answer 1

Hi Cadence,

To determine the total expenses encountered by Kara's Custom Tees, we can use the following equation:

C(x) = Fixed Costs + (Variable Costs per shirt * Number of Shirts)

In this case, the fixed costs are $500, and the variable costs per shirt are $5. So, the equation becomes:

C(x) = 500 + 5x

Now, let's calculate the cost of producing 7 shirts. To do that, plug in x = 7 into the equation:

C(7) = 500 + 5 * 7

C(7) = 500 + 35

C(7) = $535

So, the cost of producing 7 shirts for Kara's Custom Tees is $535.

I hope this helps

Answer 2

Hi Cadence,

You want an equation that describes total cost. That always means you want C(x)= “something.” Thus, left side is:

C(x)=

Now, for the rest, we know the company’s fixed cost, $500. We know they will have to pay more in variable costs beyond that, so:

C(x)= 500 +

Finally, we know they have an additional cost of $5 per shirt. We were given that x was the number of shirts, so this is:

5x

That makes our final equation:

C(x)=500 + 5x

The second part of the question essentially tells us:

x=7

since we are producing 7 shirts. Therefore, we substitute 7 for x:

C(7)=500 + 5(7)

C(7)=$535

I hope this helps.

Answer 3

In this scenario, we have to build an equation based on the information given.

We start with:

C(x) =

We can include the $500, as it is a fixed price:

C(x) = 500

Lastly we need to add the variable, the total spent on shirts at $5 each can be shown as 5 times x (the number of shirts) so our final equation is:

C(x) = 500 + 5x

Now we can use this to solve for any amount of shirts produced, or in this case we use x=7 shirts:

C(7) = 500 + 5(7)

= 500 + 35

= 535

So the total cost after producing 7 shirts is $535