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

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

by BTGmoderatorDC » Wed Aug 15, 2018 8:42 pm

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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

OA B

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by GMATGuruNY » Thu Aug 16, 2018 1:50 am
BTGmoderatorDC 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 , 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
The company requested 3 more 2¢ envelopes than 5¢ envelopes.
Let the number of 5¢ envelopes = 2, and the number of number of 2¢ envelopes = 2+3 = 5, with the result that the cost of the envelopes = (5*2) + .(2*5) = 20 cents.

A company hired a printer to produce a total of x + 1 envelopes.
Since two 5¢ envelopes = 2 and five 2¢ envelopes are produced -- for a total of 7 envelopes -- we get:
x+1 = 7
x = 6.

Which of the following denotes the cost?
Now plug x=6 into the answers to see which yields a total cost of 20 cents.
Only B works:
(7x-2)/2 = (7*6 - 2)/2 = 20.

The correct answer is B.
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by swerve » Thu Aug 16, 2018 9:11 am
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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by Scott@TargetTestPrep » Sun Aug 26, 2018 5:53 pm
BTGmoderatorDC 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 thus 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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