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Printer - envelopes

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by RikaMueller » Sun Nov 21, 2010 4:49 am
A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2$ envelopes and 5$ envelopes. If the company requested 3 more 2$ envelopes than 5$ envelopes, which of the following expression denotes the cost, in cents, of total x + 1 envelopes.

a. 3x + 1
b. (7x-2)/2
c. 11x + 31
d. (7x - 6)/2
e. (13x + 3)/2

pls explain
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by Rahul@gurome » Sun Nov 21, 2010 5:00 am
Say, number of $5 envelopes = n => Number of $2 envelopes = (n + 3)
Thus, total number of envelopes = n + (n + 3) = 2n + 3 = x + 1 => n = (x - 2)/2

Now, cost of all the envelopes = ($5)*(n) + ($2)*(n + 3) = $(5n + 2n + 6) = $(7n + 6) = $[7*{(x - 2)/2} + 6] = $[(7x - 2)/2]

The correct answer is B.

(I believe either the prices are in cents or the cost is asked in dollar. Please check the question.)
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by RikaMueller » Sun Nov 21, 2010 5:21 am
Thanks.

But from:

$[7*{(x - 2)/2} + 6] = $[(7x - 2)/2]

I would get $[(7x - 1)/2] as -14/2 + 6 = -1.
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by RikaMueller » Sun Nov 21, 2010 5:26 am
ah ok, got it. Just made a mistake. Thanks for explaining. Really helped me. :-)
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by Rahul@gurome » Sun Nov 21, 2010 5:28 am
RikaMueller wrote:Thanks.

But from:

$[7*{(x - 2)/2} + 6] = $[(7x - 2)/2]

I would get $[(7x - 1)/2] as -14/2 + 6 = -1.
Yes.
But then you have to add -1 with 7x/2, which results in [(7x/2) - 1], which is not same as (7x -1)/2! :)

Follow me,
[7*{(x - 2)/2} + 6] = [(7x - 14)/2 + 6] = [(7x/2) - 7 + 6] = [(7x/2) - 1] = [(7x - 2)/2]

Hope it helps!
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by RikaMueller » Sun Nov 21, 2010 5:31 am
yes. Thanks a lot...I saw my mistake after I posted my first reply :)
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by GMATGuruNY » Sun Nov 21, 2010 6:02 am
RikaMueller wrote:A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 2¢ envelopes and 5¢ envelopes. If the company requested 3 more 2¢ envelopes than 5¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?

A)3x+1

B)(7x-2)/2

C)11x+31

D)(7x-6)/2

E)(13x+3)/2

pls explain
We can plug in our own values:

2 5¢ envelopes requested.
5 2¢ envelopes requested (since 3 more 2¢ envelopes are requested).
2+5 = 7 total envelopes requested.
Thus, x+1 = 7, x = 6.
Cost = 2*5 +5*2 = 20. This is our target.

Now we plug x=6 into all the answer choices to see which yields our target of 20.

Only answer choice B works:
(7x-2)/2 = (7*6-2)/2 = 20.

The correct answer is B.
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