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gamjatang
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In a magazine store, magazine A is sold at $1, and magazine 15 Dec 2005, 04:51
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In a magazine store, magazine A is sold at $1, and magazine B is sold at $1.25. If this store has no other magazines except for magazine A and magazine B, magazine A is r% of the total revenue of this store and p% of the total number of magazines sold in this store.

Express r in terms of p.



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In a magazine store, magazine A is sold at $1, and magazine 15 Dec 2005, 10:22
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Na=p/100*(Na+Nb)

Nb=(100-p)/100*(Na+Nb)

Na/Nb=p/(100-p) ----> Na=Nb*p/(100-p)

On the other side, Na/(Na+1.25Nb)=r/100

Therefore (p/(100-p))Nb/(p/(100-p)+1.25)Nb=r/100 or

p/(p+1.25(100-p))=r/100

100p=rp+1.25(100-p)----> r=(100p - 1.25(100-p))/p
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In a magazine store, magazine A is sold at $1, and magazine 15 Dec 2005, 11:50
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let total number of magazine sold = x and total revenue = y

so P* x/100 = R* y/100

or x/y = R/P ...............i)

again 1.5 * (100-P)* x/100 = (100-R)* y/100

or x/y = (100-R)/(150-1.5 P) .............ii)

from i and ii

we get R/P = (100-R)/(150-1.5 P)

or R = 100 / (150- P/2)
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In a magazine store, magazine A is sold at $1, and magazine 15 Dec 2005, 17:52
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It is said that when you see this type of question during the test, then you're doing good - at least 49 in math. Thus, it would be ok to try this type of question a few times. (Of course the real questions will be easier than this one since you'll be given the answer choices)
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In a magazine store, magazine A is sold at $1, and magazine 15 Dec 2005, 18:22
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nakib77
let total number of magazine sold = x and total revenue = y

so P* x/100 = R* y/100

or x/y = R/P ...............i)

again 1.5 * (100-P)* x/100 = (100-R)* y/100

or x/y = (100-R)/(150-1.5 P) .............ii)

from i and ii

we get R/P = (100-R)/(150-1.5 P)

or R = 100 / (150- P/2)
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Nakib.. you took 1.5 instead of 1.25

Here is my answer

Total Revenue = X
Total Magzines sold = Y

For magzine A
rX/100 = (pY/100) * 1
i.e. rX = pY .................................... Equation 1

For magzine B
(100-r)X/100 = [(100-p) Y/100] * 1.25

4X(100-r) = 5Y(100-p).......................... Equation 2

Substitute value of X from eq 1 in eq 2
4pY(100-r)/r = 5Y(100-p)
4p(100-r) = 5r(100-p)
400p-4pr = 500r-5pr

r=400p/(500-p) ANS
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In a magazine store, magazine A is sold at $1, and magazine 16 Dec 2005, 10:23
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automan
Na=p/100*(Na+Nb)

Nb=(100-p)/100*(Na+Nb)

Na/Nb=p/(100-p) ----> Na=Nb*p/(100-p)

On the other side, Na/(Na+1.25Nb)=r/100

Therefore (p/(100-p))Nb/(p/(100-p)+1.25)Nb=r/100 or

p/(p+1.25(100-p))=r/100

100p=rp+1.25(100-p)----> r=(100p - 1.25(100-p))/p
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what if the number of sold magazines for A and B are different
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In a magazine store, magazine A is sold at $1, and magazine 16 Dec 2005, 11:31
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bewakoof
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Na=p/100*(Na+Nb)

Nb=(100-p)/100*(Na+Nb)

Na/Nb=p/(100-p) ----> Na=Nb*p/(100-p)

On the other side, Na/(Na+1.25Nb)=r/100

Therefore (p/(100-p))Nb/(p/(100-p)+1.25)Nb=r/100 or

p/(p+1.25(100-p))=r/100

100p=rp+1.25(100-p)----> r=(100p - 1.25(100-p))/p

what if the number of sold magazines for A and B are different
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I don't understand what you mean. Please, can you precise a bit more what you don't understand on my reasoning?
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In a magazine store, magazine A is sold at $1, and magazine 26 Dec 2005, 13:45
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let:
n : total number of magazines sold

total revenue = np + (1-p)*n*1.25 = n (1.25 - 0.25 p)

r = (A's revenue / total revenue) * 100
r = (np / n (1.25 - 0.25 p)) * 100 or

r = 100p / (1.25 - 0.25p)




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