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A company hired a printer to produce a total of x + 1 [#permalink]
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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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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*62)/2=20¢. Correct. Answer: B. Note that for plugin 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]
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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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Let the number of 2c envelopes = p 5c envelopes = q Given P = q + 3 P+q=x+1 => 2q+3 = x+1 Q = x2/2 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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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]
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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]
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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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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 start with two equations: 1. t+f=x+1 2. tf=3 adding 1 & 2 ➡ t=(x+4)/2 subtracting 2 from 1 ➡ f=(x2)/2 substituting in 2t+5f, then 2(x+4/2)+5(x2/2)=(7x2)/2



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