Problem Solving

This is taken from the Kaplan course book. There is no answer to this problem in the end of the chapter, so I tried it myself and put the answer here below, in the end of the message. I think I'm right, please correct me if I'm wrong. You can try to solve it yourself if you wish

Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month and a + b for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?

(A) (a - b)(a + b + n)
(B) a - b
(C) a² - b²
(D) n(a - b)
(E) an + bn - an

Here's how I did: Let's say the total of articles written is t. The total amount of money a writer makes is n articles × a + (t - n) × (a + b). We know there are two kinds of writers: Those who submit n + a articles, and those who submit n + b articles. Let's substitute t within the equations:

"n + a" writers make: an + (n + a - n)(a + b) dollars
"n + b" writers make: an + (n + b - n)(a + b) dollars

Let's pick numbers:

a = 10
b = 2
n = 2

And substitute:

"n + a" writers make: an + (n + a - n)(a + b) dollars
That's 20 + (10)(12) = 140 dollars

"n + b" writers make: an + (n + b - n)(a + b) dollars
That's 20 + (2)(12) = 44 dollars

In our case, "n + a" writers make 96 more dollars than "n + b" writers.

Let's find out in the answer choices. Answer choice C is a² - b², that's 100 - 4, it matches ou 96 dollar difference.