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Last Sunday a certain store sold copies of Newspaper

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Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post Updated on: 10 Aug 2015, 03:14
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Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $4 each, and the store sold no other newspapers that day. If \(r\) percent of the store's revenue 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 \(p\) in terms of \(r\)?

A. \(\frac{{100+5r}}{{400r}}\)

B. \(\frac{{400r}}{{100+5r}}\)

C. \(\frac{{100+3r}}{{400r}}\)

D. \(\frac{{400r}}{{100+3r}}\)

E. \(\frac{{100r}}{{100+5r}}\)



Question from OG 13, but with a twist. Anybody know how to solve without having to solve for \(r\) first?

Originally posted by mejia401 on 09 Aug 2015, 15:25.
Last edited by mejia401 on 10 Aug 2015, 03:14, edited 1 time in total.
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 09 Aug 2015, 23:23
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mejia401 wrote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $4 each, and the store sold no other newspapers that day. If \(r\) percent of the store's revenue 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 \(p\) in terms of \(r\)?

A. \(\frac{{1+5r}}{{400r}}\)

B. \(\frac{{400r}}{{1+5r}}\)

C. \(\frac{{1+3r}}{{400r}}\)

D. \(\frac{{400r}}{{1+3r}}\)

E. \(\frac{{100r}}{{1+5r}}\)



Question from OG 13, but with a twist. Anybody know how to solve without having to solve for \(r\) first?


The options given are not correct (I assume you have made modifications). You have assumed a fraction value for r (e.g. 1/2) and not percent value (e.g. 50).
When you say r percent in the question, you are implying that r will take values from 0 to 100. But in that case, your options are incorrect. They assume that r will take values from 0 to 1.
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 10 Aug 2015, 03:18
VeritasPrepKarishma wrote:
mejia401 wrote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $4 each, and the store sold no other newspapers that day. If \(r\) percent of the store's revenue 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 \(p\) in terms of \(r\)?

A. \(\frac{{1+5r}}{{400r}}\)

B. \(\frac{{400r}}{{1+5r}}\)

C. \(\frac{{1+3r}}{{400r}}\)

D. \(\frac{{400r}}{{1+3r}}\)

E. \(\frac{{100r}}{{1+5r}}\)



Question from OG 13, but with a twist. Anybody know how to solve without having to solve for \(r\) first?


The options given are not correct (I assume you have made modifications). You have assumed a fraction value for r (e.g. 1/2) and not percent value (e.g. 50).
When you say r percent in the question, you are implying that r will take values from 0 to 100. But in that case, your options are incorrect. They assume that r will take values from 0 to 1.



VeritasPrepKarishma Thank you :oops: . Do you think modifications to an OG question adds value to the forum (even if the answer choices are right:)?
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 10 Aug 2015, 22:25
mejia401 wrote:
VeritasPrepKarishma wrote:
mejia401 wrote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $4 each, and the store sold no other newspapers that day. If \(r\) percent of the store's revenue 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 \(p\) in terms of \(r\)?

A. \(\frac{{1+5r}}{{400r}}\)

B. \(\frac{{400r}}{{1+5r}}\)

C. \(\frac{{1+3r}}{{400r}}\)

D. \(\frac{{400r}}{{1+3r}}\)

E. \(\frac{{100r}}{{1+5r}}\)



Question from OG 13, but with a twist. Anybody know how to solve without having to solve for \(r\) first?


The options given are not correct (I assume you have made modifications). You have assumed a fraction value for r (e.g. 1/2) and not percent value (e.g. 50).
When you say r percent in the question, you are implying that r will take values from 0 to 100. But in that case, your options are incorrect. They assume that r will take values from 0 to 1.



VeritasPrepKarishma Thank you :oops: . Do you think modifications to an OG question adds value to the forum (even if the answer choices are right:)?



Yes, I advise people to think how small changes in the question can impact their solution. It helps in better understanding. Though, if you do put up such a question on the forum, I suggest you tag it as "self made" and ensure that the question stem as well as the options are correct. I am sure you wouldn't want people to worry about why their answer doesn't match any option.
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 16 Aug 2015, 16:54
mejia401 wrote:
Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $4 each, and the store sold no other newspapers that day. If \(r\) percent of the store's revenue 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 \(p\) in terms of \(r\)?

A. \(\frac{{100+5r}}{{400r}}\)

B. \(\frac{{400r}}{{100+5r}}\)

C. \(\frac{{100+3r}}{{400r}}\)

D. \(\frac{{400r}}{{100+3r}}\)

E. \(\frac{{100r}}{{100+5r}}\)



Question from OG 13, but with a twist. Anybody know how to solve without having to solve for \(r\) first?


Similar question to practice: last-sunday-a-certain-store-sold-copies-of-newspaper-a-for-101739.html
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 22 Apr 2018, 21:34
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lets assume that x no of newpaper A and Y no of newspaper B were sold.

So, r =x/(1*x+4*y) *100

and p =x/( x+y) *100


re-arranging we get,

4(x +y) =4*100* x /p

and x +4y = 100 *x/r


so, 100/r =400/p -3

or 4/p=1/r +3/100


or p=400r/(100 +3r)
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Re: Last Sunday a certain store sold copies of Newspaper  [#permalink]

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New post 23 Aug 2018, 00:08
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Let total number of copies sold be 100
No of copies of A sold be =x, then number of copies of B sold will be (100-x)

Then total revenue will be = x*1 + 4* (100-x)= 400-3x
revenue from A =r%= \(\frac{no of copies of A sold * price per copy}{ total revenue}\)
r%=\(\frac{x}{400-3x}*100\)
r= \(\frac{100x}{400-3x}\) equation (1)

p%= \(\frac{no of copies of A sold }{total no of copies sold}*100\)

p= x -------- equation (2)

Substituting (2) in (1)
r= \(\frac{100p}{400-3p}\)

then,
p=\(\frac{400r}{100+3r}\)
Re: Last Sunday a certain store sold copies of Newspaper &nbs [#permalink] 23 Aug 2018, 00:08
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