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# A company hired a printer to produce a total of x + 1

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Manager
Joined: 29 Nov 2011
Posts: 71
A company hired a printer to produce a total of x + 1  [#permalink]

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21 Feb 2012, 02:45
1
21
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Difficulty:

65% (hard)

Question Stats:

67% (02:58) correct 33% (02:55) wrong based on 393 sessions

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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

Can anyone explain using picking numbers approach?
Math Expert
Joined: 02 Sep 2009
Posts: 59721

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21 Feb 2012, 03:02
7
4
Smita04 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

Can anyone explain using picking numbers approach?

Let the # of 5¢ envelopes be 2, then # of 2¢ envelopes will be 5, total=2+5=7 envelopes: x+1=7 --> x=6.
Cost: 5¢*2+2¢*5=20¢.

Now, plug x=6 in answer choices and see which one gives 20¢:

B. (7x - 2)/2=(7*6-2)/2=20¢. Correct.

Note that for plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. For example numbers 1 and 4 gives two "correct" choices A and B.

Hope it helps.
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Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Re: A company hired a printer to produce a total of x + 1  [#permalink]

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31 May 2013, 07:18
6
1
Let the number of

2c envelopes = p
5c envelopes = q

Given

P = q + 3
P+q=x+1

=> 2q+3 = x+1

Q = x-2/2

Total cost = 2p + 5q substituting p = q+3 we get

= 7q +6 substituting for q

7x - 2/2
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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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31 May 2013, 07:19
3
Smita04 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

Can anyone explain using picking numbers approach?

Assume that no of 5 cents envelopes = 0. Thus, the no of 2 cents envelopes = 3. Total cost = 6 cents. Also, the total no of envelopes,x+1 = 3--> x=2. Only B gives 6 cents for x=2.
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GMAT Date: 06-11-2013
GPA: 3.5
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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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02 Jun 2013, 13:41
1
Let x = 6, hence x +1 = 7

the company requested 3 more 2¢ envelopes than 5¢ envelopes

let y be the number of required 5¢ envelopes,

therefore (y+3) is the required number of 2¢ envelopes

y + y + 3 = total number of envelopes = x+ 1,therefore y + y + 3 = 7

2y = 4

y = 2, (y+3) = 5

cost of 2¢ envelopes = 5 * 2 = 10 cents

cost of 5¢ envelopes = 2 * 5 = 10 cents

Total Cost = 20 cents, plugging back into the answer choices

choice b : (7x - 2)/2 = (7*6 -2)/2 = 40/2 = 20 cents
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Joined: 29 Nov 2011
Posts: 71
Re: A company hired a printer to produce a total of x + 1  [#permalink]

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21 Feb 2012, 05:18
Thanks Bunuel, it definitely helped.
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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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31 May 2013, 06:23
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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10 Jan 2014, 10:36
Smita04 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

Can anyone explain using picking numbers approach?

Yeah smart numbers works well here.

X+1 = 7
X= 6

So 2c envelopes will be 5
and 5c envelopes will be 2

So total cost will be 20

Then that is our target

Plug x =6 in answer choices

Only B works

Hope it helps
Cheers!
J
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Joined: 07 Dec 2014
Posts: 1217
A company hired a printer to produce a total of x + 1  [#permalink]

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03 Sep 2015, 11:21
let t=# two cent envelopes
let f=# five cent envelopes
total cost=2t+5f
1. t+f=x+1
2. t-f=3
adding 1 & 2 ➡ t=(x+4)/2
subtracting 2 from 1 ➡ f=(x-2)/2
substituting in 2t+5f, then 2(x+4/2)+5(x-2/2)=(7x-2)/2
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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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21 Feb 2018, 14:10
Smita04 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

We can let a = the number of 2¢ envelopes and b = the number of 5¢ envelopes:

Since the company requested 3 more 2¢ envelopes than 5¢ envelopes:

a = b + 3

Since the total number of envelopes is x + 1, we have:

a + b = x + 1

b + 3 + b = x + 1

2b = x - 2

b = x/2 - 1

Thus, a = b + 3 = x/2 - 1 + 3 = x/2 + 2.

So, in terms of x, the cost of the 2¢ envelopes is 2(x/2 + 2) cents, and the cost of the 5¢ envelopes is 5(x/2 - 1) cents, and the total cost of all the envelopes is:

2(x/2 + 2) + 5(x/2 - 1)

x + 4 + 5x/2 - 5

2x/2 + 5x/2 - 2/2

(7x - 2)/2 cents

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Re: A company hired a printer to produce a total of x + 1  [#permalink]

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29 May 2019, 08:01
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Re: A company hired a printer to produce a total of x + 1   [#permalink] 29 May 2019, 08:01
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