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
Source: Princeton Review
A company hired a printer to produce a total of x + 1
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The company requested 3 more 2¢ envelopes than 5¢ envelopes.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
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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We can let a = the number of 2¢ envelopes and b = the number of 5¢ envelopes: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
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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