Question

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 9 cds be? let x represent the number of cds over 5.
c(x) =
(type an expression using x as the variable.)

Explanation:

Step1: Identify fixed and variable costs

The fixed cost for the first 5 CDs is $29. The variable cost per additional CD is $4, and $x$ represents the number of CDs over 5.

Step2: Write the cost - function formula

The cost function $C(x)$ is the sum of the fixed cost and the variable cost. The variable cost is $4x$ (since each additional CD costs $4$ and there are $x$ additional CDs). So, $C(x)=29 + 4x$.

Step3: Calculate the value of $x$ for 9 CDs

If we want to buy 9 CDs, the number of CDs over 5 is $x=9 - 5=4$.

Step4: Substitute $x$ into the cost - function

Substitute $x = 4$ into $C(x)=29+4x$. Then $C(4)=29+4\times4$.
$C(4)=29 + 16$.
$C(4)=45$.

Answer:

$C(x)=29 + 4x$; The cost of buying 9 CDs is $45$.