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Each writer for the local newspaper is paid as follows: a

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Each writer for the local newspaper is paid as follows: a [#permalink] New post 05 Feb 2005, 13:52
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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?

1) (a-b)(a+b+n)
2) a-b
3) a^2-b^2
4) n(a-b)
5) an+bn-an

Is there an easier way than picking #'s.
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Re: Kaplan PS Algebra [#permalink] New post 05 Feb 2005, 19:18
=na+a(a+b)-[na+b(a+b)]
=na+a^2+ab-na-ab-b^2
=a^2-b^2
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Re: Kaplan PS Algebra [#permalink] New post 05 Feb 2005, 20:00
willgoldberg wrote:
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?

1) (a-b)(a+b+n)
2) a-b
3) a^2-b^2
4) n(a-b)
5) an+bn-an

Is there an easier way than picking #'s.


(n+a)*a+ab-[(n+b)*a+b*b]
=na+a^2+ab-na-ab-b^2
=a^2-b^2

(3)
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 [#permalink] New post 06 Feb 2005, 22:47
yes, you don't have to pick numbers:
submit n+a stories
na + (a+b)a = na + a^2 +ab

submit n+b stories
na + (a+b)b = na + ab + b^2

Difference:

na + a^2 +ab - na -ab - b^2 = a^2 - b^2 --> (3)
  [#permalink] 06 Feb 2005, 22:47
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