Recycled​ CDs, Incorporated, offers a choice of 5 used CDs for ​$29​, with each additional CD costing ​$4. Write a cost function for purchasing 5 or more CDs. What will the cost of buying 12 CDs​ be? Let x represent the number of CDs over 5.


To solve this problem, let's break it down into two parts: writing the cost function and then calculating the cost for purchasing 12 CDs.

### Step 1: Writing the Cost Function

Recycled CDs, Incorporated, offers the first 5 CDs for a fixed price of $29. Any additional CD beyond these 5 costs $4 each.

Let $ x $ represent the number of CDs beyond the initial 5.

- The total number of CDs is $ 5 + x $.
- The cost for the first 5 CDs is $29.
- The cost for the additional $ x $ CDs is $ 4x $ (since each additional CD costs $4).

The total cost function $ C(x) $ for purchasing 5 or more CDs can be expressed as:

\[
C(x) = 29 + 4x
\]

### Step 2: Calculating the Cost for 12 CDs

If a customer buys 12 CDs, then $ x $ (the number of CDs beyond the initial 5) would be:

\[
x = 12 - 5 = 7
\]

Now, substitute $ x = 7 $ into the cost function $ C(x) $:

\[
C(7) = 29 + 4(7) = 29 + 28 = 57
\]

So, the cost of buying 12 CDs is **$57**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would the cost function change if the price per additional CD was different?
2. What would the cost be for 8 CDs?
3. How does the cost function behave as the number of CDs increases indefinitely?
4. If you had a budget of $100, how many CDs could you buy?
5. How would the equation change if the first 5 CDs were free?

**Tip:** Understanding how to set up a cost function helps in solving a variety of real-world problems where pricing changes after a certain quantity.

Recycled CDs, Incorporated, offers a choice of 5 used CDs for ​$29​, with each additional CD costing ​$4. Write a cost function for purchasing 5 or more CDs. What will the cost of buying 12 CDs​ be? Let x represent the number of CDs over 5.

Discover how to write a cost function for purchasing CDs from Recycled CDs, Incorporated. Understand the pricing model and learn how to calculate the total cost for 12 CDs using linear functions. Perfect for students in Grades 6-8.

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