Problem Solving

mitzwillrockgmat 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)

Total no of newspaper sold = 100x, A newspaper = px, B = 100x-px
Rev from A = $px Rev from B = $100x-px*1.25 Tot rev = px+125x-1.25px = 125x-0.25px
px/125x-0.25px= r/100,
r=100px/(125x-px/4)
r= 400px/(500-px) = 400p/(500-p)

Phew ! on second attempt

For a detailed explanation, please see the attached.

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

Just one thing i don't understand is that since P is a percentage as well, why you just use 100 - P but not 100 - 100P or 100*(1-P)? I know for r, we do need P / 125-.025p to mutlitply 100 since r is a percentage. Could you please let me know?

Thanks

mitzwillrockgmat 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)

Please help! Need a simple solution to this! thanks!

Let:
The number of copies of A sold = 1.
The number of copies of B sold = 4.

Total copies sold = 1+4 = 5.
Since A = 1/5 of the copies sold, p = 1/5*100 = 20.

Revenue from 1 copy of A = $1.
Revenue from 4 copies of B = 4*1.25 = $5.
Total revenue = 1+5 = 6.
Since A = 1/6 of the total revenue, r = 1/6*100 = 50/3. This is our target.

Now we plug p=20 into all the answers to see which yields our target of 50/3.

Only answer choice D works:
(400*20)/(500-20) = 8000/480 = 50/3.

The correct answer is D.

I've thought of a method but would like someone to see if it is a correct way of approaching it.
I've immediately assumed total qty of newspaper sold is 100, given the entire question is asking about r in terms of p, we can see from here that no matter what we assign as total qty, in the end once it is back to a %, the value for P is all the same.

Price A: $1.00
Qty A : p
Rev A : r

Price B: $1.25
Qty B : 100 - p


r = (rev A) / (rev A + rev B) * 100%

r = $1.00*P / ($1.00*P + $1.25 * (100-P)) *100%

r = P/(125-0.25P) * 100% (multiply top and bottom of fraction by 4)

r = 4p / (500 - p) *100%

r = 400p / (500-p)

kaihsin wrote:I've thought of a method but would like someone to see if it is a correct way of approaching it.
I've immediately assumed total qty of newspaper sold is 100, given the entire question is asking about r in terms of p, we can see from here that no matter what we assign as total qty, in the end once it is back to a %, the value for P is all the same.

Price A: $1.00
Qty A : p
Rev A : r

Price B: $1.25
Qty B : 100 - p


r = (rev A) / (rev A + rev B) * 100%

r = $1.00*P / ($1.00*P + $1.25 * (100-P)) *100%

r = P/(125-0.25P) * 100% (multiply top and bottom of fraction by 4)

r = 4p / (500 - p) *100%

r = 400p / (500-p)

Nice work!