Problem Solving

It costs x dollars each to make the first 1,000 copies of a compact disc and y dollars to make each subsequent copy. If z is greater than 1,000, how many dollars will it cost to make z copies of the compact disc?

(A) 1,000x + yz
(B) zx - zy
(C) 1,000 (z - x) + xy
(D) 1,000 (z - y) + xz
(E) 1,000 (x - y) + yz

The OA is the option E.

How can I get the last expression? Could someone help me? Please. I'd be thankful.

Hello Vjesus12.

Let's take a look at your question.

We know the following:

- It costs x dollars to make each of the first 1,000 copies.
- It costs y dollars to make each subsequent copy.
- z is greater than 1,000.

Now, the cost for the first 1,000 copies is equal to 1,000*x.

The number of copies over 1,000 is given by z-1,000. Since the cost for the rest of the copies is y dollars, then the cost to make the excess of copies (over 1,000) is given by
$$\left(z-1,000\right)\cdot y.$$ Therefore, the total cost is given by $$1,000\cdot x+\left(z-1,000\right)\cdot y=1,000\cdot x+z\cdot y-1,000\cdot y=1,000\left(x-y\right)+yz.$$ This implies that the correct answer is the option E.

I hope it helps you. <i class="em em-smiley"></i>