picking numbers and variable choices

[martinho]

Hello,
I don't understand how to solve this problem:
Each writer of 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


I've got the answer but not the explanation.
I really need to develop my ability to put words into equations but that's still difficult for me.
This question is rated as advanced by Kaplan.

Cheers!

[Vemuri]

Answer should be C.

For these type of questions, plugging in values will be the easiest & fastest way of solving.

Lets assume a=$10, b=$5, n=5 stories

For (n+a)=15 stories, the dollars earned is $10+10*$15=$160
For (n+b)=10 stories, the dollars earned is $10+5*$15=$85
Difference = $160 - $85 = $75

Now, input these variable values in the answer choices & observe only C equals $75.

Hope this helps.

[martinho]

Cheers mate!
I've figured out that I often look for difficulty into questions.
That's weird.
I may have done it because of kaplan's book: you can see the difficulty level in the margin...
Thanks again

[lilu]

Or you can actually translate word into equations:
an per story
a+b per additional story
Now, for the first writer:
na+(n+a)(n+b)=2an+bn+a^2+ab

For the second writer:
na+(n+b)(a+b)=2an+ab+b^2+bn

Now, we need to find the difference and we know that a>b, so subtract second expression from first and you' ll get a^2-b^2
And that's your answer