Bunuel wrote:
An agent was billed a total of $6.00 for n reams of paper. As a result of a price increase of $0.25 per ream, the agent's next bill of $6.00 was for 4 fewer reams of paper. The second bill was for how many reams of paper?
A. 8
B. 12
C. 24
D. 25
E. 48
PS20419
Alternative method:
Let's say that
n = quantity of reams of papers
p = price per each ream
FORMULA 1: P(N) = $6
As a result of a price increase of $0.25 per ream, the agent's next bill of $6.00 was for 4 fewer reams of paper.If P is increased by 0.25 cents, n decrease by 4, but still equals to 6. When we translate that into math.
FORMULA 2: (P + 0.25)(N - 4) = $6
We can use the answer choices to help us solve this problem
Let's choose choice B, or 12.
The second bill is N - 4, which equals 12. So N =16
Plug N=16 to the first formula
P(16) = 6
P = \(\frac{6}{16}\)
P = \(\frac{3}{8}\)
Plug in \(\frac{3}{8}\) into the second formula
(3/8 + 1/4)(12) = $6
Divide 12 on each side and add the fractions together
Does \(\frac{5}{8}\) = \(\frac{1}{2}\)? Clearly NO, so B is incorrect. But it tells us that we need to increase the right hand [\(\frac{1}{2}\)] side. The only way to do to so is to reduce (N - 4),
so the answer has to be A!______________
If you didn't realize that, you can test answer choice D to determine that pattern
P(n) = 6
(P + 0.25)(N - 4) = $6
N - 4 = 25, so N = 29
P(29) = 6
P = \(\frac{6}{29}\)
Plug P into the 2nd formula
(6/29 + 1/4)(25) = $6
Divide 25 by each side and add the fractions together
\(\frac{53}{116}\) = \(\frac{24}{100}\)
Clearly they're not equal, but the difference between \(\frac{53}{116}\) and \(\frac{24}{100}\) is much larger than \(\frac{5}{8}\) and \(\frac{1}{2}\) from Answer Choice B