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 help! Need a simple solution to this! thanks!

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)

p : store sold paper A
100 -p : store sold paper B

total revenues : p *1 + (100 -P)*1.25 = 125 - 0.25P
r = (P/(125 - 0.25p) )* 100
r = 400P/(500 - P) Hence ANS D

Let the store sold total p copies of A and 100-p copies of B.So,total revenue is
p+1.25(100-p)

and {p+1.25(100-p)}*r/100=p...
or (125-0.25p)*r=100p
or (500-p)*r=400p
or r=400p/(500-p)

Ans option D

liferocks wrote:Let the store sold total p copies of A and 100-p copies of B.So,total revenue is
p+1.25(100-p)

and {p+1.25(100-p)}*r/100=p...
or (125-0.25p)*r=100p
or (500-p)*r=400p
or r=400p/(500-p)

Ans option D

hi, can you please explain this without using P as the no. of copies sold of newspaper A. it really confuses the calculation & that is why i havent been able to understand previous posts regarding this question. already have p% to consider by considering p as copies of A it muddles up the calculations. thanks!

mitzwillrockgmat wrote: hi, can you please explain this without using P as the no. of copies sold of newspaper A. it really confuses the calculation & that is why i havent been able to understand previous posts regarding this question. already have p% to consider by considering p as copies of A it muddles up the calculations. thanks!

Ok. Lets take total number of copies sold for A 100x and for B is 100y
so total copies sold is 100x+100y

Since p% of it is copies of A, we get px+py=100x..or y/x=(100-p)/p

total revenue 100x+125y..r% of it is from A
hence rx+5ry/4=100x
so rx+5ry/4=px+py or 4rx+5ry=4px+4py or 4x(r-p)=y(4p-5r)
or y/x=4(r-p)/(4p-5r)=(100-p)/p
or 4rp-4p^2=400p-4p^2-500r+5rp
or rp-500=-400p
or r=400p/(500-p)

Let me know if this helps..but I personally feel that this is much more complected than the first approach.

liferocks wrote:

mitzwillrockgmat wrote: hi, can you please explain this without using P as the no. of copies sold of newspaper A. it really confuses the calculation & that is why i havent been able to understand previous posts regarding this question. already have p% to consider by considering p as copies of A it muddles up the calculations. thanks!

Ok. Lets take total number of copies sold for A 100x and for B is 100y
so total copies sold is 100x+100y

Since p% of it is copies of A, we get px+py=100x..or y/x=(100-p)/p

total revenue 100x+125y..r% of it is from A
hence rx+5ry/4=100x
so rx+5ry/4=px+py or 4rx+5ry=4px+4py or 4x(r-p)=y(4p-5r)
or y/x=4(r-p)/(4p-5r)=(100-p)/p
or 4rp-4p^2=400p-4p^2-500r+5rp
or rp-500=-400p
or r=400p/(500-p)

Let me know if this helps..but I personally feel that this is much more complected than the first approach.

ummm still dont get it!! i dunno the calculation in this question dont make sense to me at all!

r% + p% =100% or r +p =1 is there a solution along these lines maybe??

im just not getting how i can find r% of a number in terms of p% ...how do i equate the two?

.let me know if you come up with a alternate approach but thanks for ltrying!

mitzwillrockgmat wrote:
r% + p% =100% or r +p =1 is there a solution along these lines maybe??

this is not correct.Because r is the percentage of total revenue from A
And p is the percentage of total copies sold for A.
Keeping this in mind you may be try to go with the approach u find find suitable.Just try to eliminate all variables other than r and p. if you post your approach I can try to help

liferocks wrote:

mitzwillrockgmat wrote:
r% + p% =100% or r +p =1 is there a solution along these lines maybe??

this is not correct.Because r is the percentage of total revenue from A
And p is the percentage of total copies sold for A.
Keeping this in mind you may be try to go with the approach u find find suitable.Just try to eliminate all variables other than r and p. if you post your approach I can try to help

ok first i realised that i didnt understand what p actually was! so thanks for pointing that out!

now knowing what p & r are i proceeded like this...

newspaper a b
price 1 1.25
qty sold x y

total revenue x + 1.25y

r% is stores revenue from A so;

r= x/(x+1.25y)

p% of the newspapers sold = A qty so:

p(x+y) = x

so now, i will subsitute x= px +py into

r= x/(x+1.25y)

i get :

r = px +py / (px +py +1.25y)

now what?? how do i simplify further??
even if i take 100x & 100y as the quantities i end up at the same point. pls show me how! thanks

mitzwillrockgmat wrote: now knowing what p & r are i proceeded like this...

newspaper a b
price 1 1.25
qty sold x y

total revenue x + 1.25y

r% is stores revenue from A so;

r= 100x/(x+1.25y)

p% of the newspapers sold = A qty so:

p(x+y)/100 = x or p(x+y)=100x

so now, i will subsitute x= px +py into

r= 100x/(x+1.25y)

i get :

r = px +py / (x +1.25y)

Some small corrections in the calculation marked in red. Ok,now the goal is to remove x and y from the last equation.
we can re-write the equation as

r=4p(x+y)/(4x+5y)
or r=4p/{4+y/(x+y)}...1
Since we have to get r in terms of p,we will try to replace x and y in terms of p
we have p(x+y)=100x
or 100/p=1+y/x
or 100/p-1=y/x
or 100-p/p=y/x
or (100-p)/100=y/x+y...2

now substituting the value of y/x+y from 2 in equation 1 we get
r=4p/{4+(100-p)/100}
or r=400p/(400+100-p)
or r=400p/(500-p)

Any way you proceed only thing to remember is ,we have to express all variables in terms of r and p so that we can get a final expression which will have only r and p.Let me know if it is clear now.

liferocks wrote:

mitzwillrockgmat wrote: now knowing what p & r are i proceeded like this...

newspaper a b
price 1 1.25
qty sold x y

total revenue x + 1.25y

r% is stores revenue from A so;

r= 100x/(x+1.25y)

p% of the newspapers sold = A qty so:

p(x+y)/100 = x or p(x+y)=100x

so now, i will subsitute x= px +py into

r= 100x/(x+1.25y)

i get :

r = px +py / (x +1.25y)

Some small corrections in the calculation marked in red. Ok,now the goal is to remove x and y from the last equation.
we can re-write the equation as

r=4p(x+y)/(4x+5y)
or r=4p/{4+y/(x+y)}...1
Since we have to get r in terms of p,we will try to replace x and y in terms of p
we have p(x+y)=100x
or 100/p=1+y/x
or 100/p-1=y/x
or 100-p/p=y/x
or (100-p)/100=y/x+y...2

now substituting the value of y/x+y from 2 in equation 1 we get
r=4p/{4+(100-p)/100}
or r=400p/(400+100-p)
or r=400p/(500-p)

Any way you proceed only thing to remember is ,we have to express all variables in terms of r and p so that we can get a final expression which will have only r and p.Let me know if it is clear now.

ok , last question...how did u simplify the values in red to r=4p(x+y)/(4x+5y) ?? thanks for helping out!

mitzwillrockgmat wrote:
ok , last question...how did u simplify the values in red to r=4p(x+y)/(4x+5y) ?? thanks for helping out!

r= 100x/(x+1.25y)
or r(x+1.25y)=100x..1

p(x+y)/100 = x or p(x+y)=100x ...2

Equating 1 and 2

p(x+y)=100x=r(x+1.25y)
or p(x+y)=r(x+5y/4)
or 4p(x+y)=r(4x+5y)
or r=4p(x+y)/(4x+5y)

liferocks wrote:

mitzwillrockgmat wrote:
ok , last question...how did u simplify the values in red to r=4p(x+y)/(4x+5y) ?? thanks for helping out!

r= 100x/(x+1.25y)
or r(x+1.25y)=100x..1

p(x+y)/100 = x or p(x+y)=100x ...2

Equating 1 and 2

p(x+y)=100x=r(x+1.25y)
or p(x+y)=r(x+5y/4)
or 4p(x+y)=r(4x+5y)
or r=4p(x+y)/(4x+5y)

i know you will virtually kill me now but....

how did you manipulate r= 4p(x+y) / 4x + 5y

into the answer form 400p/500-p ?

i mean dont know how to cancel x & y in the
r= 4p(x+y) / 4x + 5y equation.

thanksssss alot!!!!

mitzwillrockgmat wrote: i know you will virtually kill me now but....

how did you manipulate r= 4p(x+y) / 4x + 5y

into the answer form 400p/500-p ?

i mean dont know how to cancel x & y in the
r= 4p(x+y) / 4x + 5y equation.

thanksssss alot!!!!

r=4p(x+y)/(4x+5y)
or r=4p/{4+y/(x+y)}...1...(dividing numerator and denominator by x+y)

Since we have to get r in terms of p,we will try to replace x and y in terms of p
we have p(x+y)=100x
or 100/p=1+y/x..dividing both sides by px
or 100/p-1=y/x
or 100-p/p=y/x
or p/100-p=x/y
or 1+p/100-p=1+x/y
or (100-p+p)/(100-p)=(y+x)/y
or 100/(100-p)=(y+x)/y
or (100-p)/100=y/x+y...2..taking inverse of both sides

now substituting the value of y/x+y from 2 in equation 1 we get
r=4p/{4+(100-p)/100}
or r=400p/(400+100-p)
or r=400p/(500-p)

liferocks wrote:

mitzwillrockgmat wrote: i know you will virtually kill me now but....

how did you manipulate r= 4p(x+y) / 4x + 5y

into the answer form 400p/500-p ?

i mean dont know how to cancel x & y in the
r= 4p(x+y) / 4x + 5y equation.

thanksssss alot!!!!

r=4p(x+y)/(4x+5y)
or r=4p/{4+y/(x+y)}...1...(dividing numerator and denominator by x+y)

Since we have to get r in terms of p,we will try to replace x and y in terms of p
we have p(x+y)=100x
or 100/p=1+y/x..dividing both sides by px
or 100/p-1=y/x
or 100-p/p=y/x
or p/100-p=x/y
or 1+p/100-p=1+x/y
or (100-p+p)/(100-p)=(y+x)/y
or 100/(100-p)=(y+x)/y
or (100-p)/100=y/x+y...2..taking inverse of both sides

now substituting the value of y/x+y from 2 in equation 1 we get
r=4p/{4+(100-p)/100}
or r=400p/(400+100-p)
or r=400p/(500-p)

wow thanks! this is very confusing! im going to review al these posts again & get back to you with any more issues!! hopefully not! thanks soo much!!

you are always welcome ..I will advise you to try to deduct yourself all the steps from scratch.That will be helpful.