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Last Sunday a certain store sold copies of Newspaper A for

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Senior Manager
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Last Sunday a certain store sold copies of Newspaper A for [#permalink] New post 15 Sep 2007, 14:39
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A
B
C
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: Set 6, Q28 - Word Translation [#permalink] New post 15 Sep 2007, 16:20
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gluon 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)


I got D,

Given:
A- # of A newspapers
B- # of B newspapers

Stem says;

R(a)=100*A
R(b)=125*B
R(a) and R (b) revenues from sale of a and b newspapers respectively.

r/100=R(a)/ (R(a)+R(b))
p/100=A/ (A+B)

Solution:

100/r=(R(a)+R(b))/R(a)= 1+R(b)/R(a)= 1+ 125B/100A------>
100/r=1+5/4 (B/A)

100/p=(A+B)/A=1+B/A------> B/A=100/p-1

Plug in B/A=100/p-1 into 100/r=1+5/4 (B/A) and solve for r

it comes to D
=)
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 [#permalink] New post 15 Sep 2007, 21:43
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Wow that's brilliant Irina!! I got till r/100=R(a)/ (R(a)+R(b)) and
p/100=A/(A+B), then stared at that problem for 10 minutes before giving up.
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Re: PS: Set 6, Q28 - Word Translation [#permalink] New post 16 Sep 2007, 02:15
Let the no. of papers be A and B.
p= A/(A+B)*100 =>100/p=1+B/A
r= A/(A+1.25B)*100=>100/r=1+1.25B/A
100/r=1+1.25B/A=1+1.25(100/p-1)
100/r=(125-0.25p)/p
r=100p/(125-0.25p) which is the same as D
gluon 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)
Re: PS: Set 6, Q28 - Word Translation   [#permalink] 16 Sep 2007, 02:15
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