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

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Smita04
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A company hired a printer to produce a total of x + 1 [#permalink] New post   21 Feb 2012, 02:45
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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?
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B
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Bunuel
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Re: Word Problem [#permalink] New post   21 Feb 2012, 03:02
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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.

Answer: B.

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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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   31 May 2013, 07:18
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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] New post   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] New post   31 May 2013, 06:23
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE
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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   31 May 2013, 07:19
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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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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   02 Jun 2013, 13:41
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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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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   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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A company hired a printer to produce a total of x + 1 [#permalink] New post   03 Sep 2015, 11:21
let t=# two cent envelopes
let f=# five cent envelopes
total cost=2t+5f
start with two equations:
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] New post   21 Feb 2018, 14:10
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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

Answer: B
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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   15 Nov 2020, 00:51
Total No. of 5 cent envelopes = N

Then total No. of 2 cent envelopes = N + 3
____________________________________
Total Quantity of Envelopes = N + (N + 3) = 2N + 3

Total Cost of Envelopes in cents = 2(N + 3) + 5(N)


we need to Solve this in terms of X

We are told that the Total Quantity of Envelopes = X + 1

We determined above that the Total Quantity of Envelopes = 2N + 3

2N + 3 = X + 1

N = (X - 2)/2

(N + 3) = (X - 2)/2 + (6/2) = (X + 4)/2


Total Cost = 2 * (N + 3) + 5 * (N)

Total Cost = 2 * (X + 4)/2 + 5 * (X - 2)/2

= (2X + 8 + 5X - 10) / 2

= (7X - 2)/2

-B-
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A company hired a printer to produce a total of x + 1 [#permalink] New post   01 Jul 2021, 10:53
Coming at this a little late - but I split it into 2 parts.

Part 1: For each 5cent envelope, they are also printing a 2cent envelope.
Part 2: They are also printing 3 additional 2cent envelopes.

Therefore, for Part 1, I took the total number of envelopes (x+1), deducted 3 --> (x+1-3) and multiplied it by 7 cents and divided by 2 (for each 5cent + 2cent pair).
As a result, the equation for Part 1 is \(\frac{7}{2} * (x+1-3) = \frac{7}{2} * (x-2)\)

For Part 2: Simply 3 * 2cents = 6

When I combined parts 1 and 2, I got \(\frac{7}{2} * (x-2) + 6 = \frac{(7x-14)}{2} + \frac{12}{2} = \frac{(7x-2)}{2}\)
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Re: A company hired a printer to produce a total of x + 1 [#permalink] New post   28 Oct 2023, 23:50
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Re: A company hired a printer to produce a total of x + 1 [#permalink]
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