Problem Solving

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)

Please correct the last line of the Question..

apuso 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)

If M is the nof copies sold for News Paper A and N is the number of copies sold for Newspaper B

r = M/(M*1+N*1.25)
p = M/(M+N)

1/r = (1+1.25 N/M)
1/p = (1+N/M)

1/r = (1+ 1.25 (1/p-1))
= (1+ 1.25(1-p)/p)
= (-0.25p +1.25)/p

r = p /(-0.25p+1.25)
= 400p/(500-100p)

Which is the same as option D; since question asked to treat p and q as percentages and I treated it as fraction, a factor of 100 is coming along with p.

apuso 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)

For minimalism and upkeep of time, we must let the total number of newspapers that the store sold to be 100, and decipher what is in between the lines of the question stem in our good turn, like the meanings of the useful terms used in the question, see what I did bold in your script. Ask again if you still have any problem in accepting copies of Newspaper A to be p in number, copies of Newspaper B to be (100 - p) in number, the store's revenues to be 125 - 0.25 p in dollars, and the newspapers that the store sold to be exactly what we started with, yes 100.

Now, only read "r percent of the store's revenues from newspaper sales was from Newspaper A" and write:

(r/100) (125 - 0.25 p) = p

or r = (100 p)/(125 - 0.25 p)

more simply, r = (400 p)/(500 - p), D.

Amazing explanation sanju
must say its a very wordy problem...

I got it wrong though

How did u get 125-0.25p????

sanju09 wrote:

apuso 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)

For minimalism and upkeep of time, we must let the total number of newspapers that the store sold to be 100, and decipher what is in between the lines of the question stem in our good turn, like the meanings of the useful terms used in the question, see what I did bold in your script. Ask again if you still have any problem in accepting copies of Newspaper A to be p in number, copies of Newspaper B to be (100 - p) in number, the store's revenues to be 125 - 0.25 p in dollars, and the newspapers that the store sold to be exactly what we started with, yes 100.

Now, only read "r percent of the store's revenues from newspaper sales was from Newspaper A" and write:

(r/100) (125 - 0.25 p) = p

or r = (100 p)/(125 - 0.25 p)

more simply, r = (400 p)/(500 - p), D.

How did u get 125-0.25p????

Out of 100 Newspapers, p were sold @1 dollar each raising a revenue of $p and (100 - p) were sold @ 1.25 dollar each raising a revenue of $(125 - 1.25 p).

Thus total revenue = $(p + 125 - 1.25 p) = $(125 - 0.25 p).

sanju09 wrote:

How did u get 125-0.25p????

Out of 100 Newspapers, p were sold @1 dollar each raising a revenue of $p and (100 - p) were sold @ 1.25 dollar each raising a revenue of $(125 - 1.25 p).

Thus total revenue = $(p + 125 - 1.25 p) = $(125 - 0.25 p).

Sorry, this may be annoying, but I'm still not seeing where 125-0.25p came from. Is there another way to explain it? Thanks

Concordio wrote:

sanju09 wrote:

How did u get 125-0.25p????

Out of 100 Newspapers, p were sold @1 dollar each raising a revenue of $p and (100 - p) were sold @ 1.25 dollar each raising a revenue of $(125 - 1.25 p).

Thus total revenue = $(p + 125 - 1.25 p) = $(125 - 0.25 p).

Sorry, this may be annoying, but I'm still not seeing where 125-0.25p came from. Is there another way to explain it? Thanks

When we see variable(s) in the answer, we PLUG IN. Let's assign 100 for the total number of the papers that the store sold and some number for p, say p = 60, revenue $60, then B would be 40 in number, revenue $50; total revenue = $60 + $50 = $110.

Now the required percent (r) is = (60/110)*100 = 600/11, slightly less than 60 is our target answer.

Test choices plugging p = 60 in:

A. 100*60 / (125 - 60) = 1200/13 ELIMINATE
B. 150*60 / (250 - 60) = 900/19 ELIMINATE
C. 300*60 / (375 - 60) = 200/7 ELIMINATE
D. 400*60 / (500 - 60) = 600/11 MATCHING so keep it
E. 500*60 / (625 - 60) = 2000/39 ELIMINATE and [spoiler]pick D[/spoiler]

Algebraic detailed explanation