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

Question

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?

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?

Bunuel · Accepted Answer

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.

Transcendentalist · Answer

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

Smita04 · Answer

Thanks Bunuel, it definitely helped.

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an    alternative    solution!

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mau5 · Answer

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.

shivanigs · Answer

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

jlgdr · Answer

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

gracie · Answer

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

JeffTargetTestPrep · Answer

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

Fdambro294 · Answer

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-

perskbot · Answer

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}

bumpbot · Answer

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

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