Question

RecycledCDs, Incorporated, offers a choice of 5 used CDs for $23, With each additional CD costing $7. 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.

Answer 1

`C(n)= 7n - 12` -- Cost Function

Cost of buying 12CDs is $72

Explanation:

Given

`Base\ Amount = \$23`

`Additional\ CD\ Amount = \$7`

Solving (a): Cost Function

Let n represent CDs greater than 5

`Cost Function = Base Amount + Additional\ CD\ Amount * (n - 5)`

Substitute:

`Base\ Amount = \$23` and
`Additional\ CD\ Amount = \$7`

`Cost\ Function = 23 + 7 * (n - 5)`

`Cost\ Function = 23 + 7(n - 5)`

Open Bracket

`Cost\ Function = 23 + 7n - 35`

Collect Like Terms

`Cost\ Function = 7n - 35 + 23`

`Cost\ Function = 7n -12`

`C(n)= 7n - 12`

Solving (b): When n = 12

Substitute 12 for n in
`C(n)= 7n - 12`

`C(12) = 7 * 12 -12`

`C(12) = 84 - 12`

`C(12) = 72`

Cost of buying 12 CDs is $72