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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 05 May 2006, 20:55
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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: Newspapers. [#permalink] New post 06 May 2006, 10:25
M8 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 B, 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 am assuming you meant newspaper B where highlighted.
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Re: PS: Newspapers. [#permalink] New post 06 May 2006, 12:06
pesquadero wrote:
M8 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 B, 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 am assuming you meant newspaper B where highlighted.


No the question is correct. We need to consider revenues and the # of copies.

Let a = # of newpapers sold for type A
Let b = # of newpapers sold for type B

So equation for revenues: r = [a.1/(a.1+b.125)]*100 ---(I)
So equation for # of copies: p = [a/(a+b)]*100 ---(II)

Eliminate b/a from both the equations.

From (I) (a+1.25b)/a = 100/r ==> b/a = 0.8*(100 - r)/r ------(III)

From (II) b/a = (100 - p)/p ---(IV)

Combine (III) and (IV). We get 0.8*(100 - r )/r = (100 - p)/p.
Simplify and we get r = 400p / (500 – p). So answer is D.

Does this make sense?
_________________

Thanks,
Zooroopa

Re: PS: Newspapers.   [#permalink] 06 May 2006, 12:06
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