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Last Sunday a certain store sold copies of Newspaper A for

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Last Sunday a certain store sold copies of Newspaper A for [#permalink] New post 14 Jun 2007, 15:19
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D
E

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Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

A. 100p / (125 – p)
B. 150p / (250 – p)
C. 300p / (375 – p)
D. 400p / (500 – p)
E. 500p / (625 – p)
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Re: PS-newspaper [#permalink] New post 14 Jun 2007, 16:20
adub35 wrote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store’s revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

A. 100p / (125 – p)
B. 150p / (250 – p)
C. 300p / (375 – p)
D. 400p / (500 – p)
E. 500p / (625 – p)


D. By Plug-in numbers.

Let’s say that the number of Newspapers sold was:
A: 10
B: 40

10+40(5/4)=60

r=100/6=50/3
p=100/5=20

Then using the answers I get D.
8000/480=50/3 = r
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 [#permalink] New post 14 Jun 2007, 21:07
Yup agree with D. A real pain to work out though. Had to resort to back solving in the end.

Assuming A and B are equal,

Basically p = 50 % and r = 400/9% and then applying it to the answers in ABCDE.
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 [#permalink] New post 14 Jun 2007, 21:54
backsolving seems a really good approach here
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 [#permalink] New post 15 Jun 2007, 08:12
Took me a while, but here's how to do it without backsolving:

A: Price=$1, Percent of total sales = p/100
B: Price = $1.25, Percent of total sales = (100-p)/100

Now r% of all sales came from paper A. This means

r/100 = sales from A / (sales from A + sales from B)
r/100 = (p/100)/( p/100 + 1.25*(100-p)/100)
r/100 = p/(125 -.25p)
r/100 = (4p/ [4*(125-.25p)]) ... multiply by 4/4 to get rid of decimal
r/100 = 4p / (500-p)
r = 400p / (500 -p)
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 [#permalink] New post 15 Jun 2007, 09:23
Amazing question. Adub where did u get this question from ?
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 [#permalink] New post 10 Sep 2007, 19:03
thought it was easier to do by working out instead of backsolving-

# of newspaper A= p
# of newspaper B= 100-p

revenue from A= 1*p
revenue from B= (100-p)*1.25= 125- 1.25p
total revenue= 125- 0.25p
therefore,
r/100*(125-0.25p) = p
r= 100p/((500-p)/4)
r= 400p/500-p
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 [#permalink] New post 13 Sep 2007, 00:52
i plugged in r = 100 and p = 100...its an easy D
  [#permalink] 13 Sep 2007, 00:52
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