Word Translation

[rintoo22]

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)
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Solution which has not worked. Kindly assist

Store
Newspaper A : x copies for $1
Newspaper B : y copies for $1.25

If r percent of the store's revenues from newspaper sales was from Newspaper A
r/100 * (($1*x) + ($1.25 * y)) = $1 * x ------ 1st Equation

if p percent of the newspapers that the store sold were copies of newspaper A
p/100 * (x + y) = x ------------- 2nd equation

Therefore expresses r in terms of
r/100 * (($1*x) + ($1.25 * y)) = p/100 * (x + y)

r(($1*x) + ($1.25 * y)) = (x + y)p

But I cannot solve beyond this point to arrive to a solution..... Please help

[Anju@Gurome]

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?

The trick to solve any problem, specially the problems that involves percentages, is to pick some easy numbers without violating any conditions. Introducing unnecessary variables complicates everything. And for problems that involves percentages, always try to pick the number 100 as it makes percentage calculation very easy.

We can assume that the total number of newspapers sold by the store = 100
So, number of newspaper A sold = p% of 100 = p
Number of newspaper B sold = 100 - p

It is given that r% of total revenue from papers comes from selling newspaper A.
Revenue from A = p * 1 and revenue from B = (100 - p) * 1.25
So, total revenue from papers = p * 1 + (100 - p) * 1.25 = 125 - 0.25p

Now percentage of total revenue coming from A = (Revenue from A /Total revenue) * 100 = p/(125 - 0.25p) * 100
But it's given that p/(125 - 0.25p) * 100 = r
Now all the answer options have p in the denominator, so we'll have to remove 0.25 from the denominator. Multiplying by 400 removes 0.25
Hence, r = 400p/(500 - p)

The correct answer is D.

[GMATGuruNY]

Last Sunday a certain store sold copies of Newspaper A for $1 and Newspaper B for 1.25. If r percent of the stores revenue came from newspaper sales of Paper A and if p percent of the newspapers sold that day were A, which of the following expresses r in terms of p?

100p/125-p
150p/250-p
300p/375-p
400p/500-p
500p/625-p

Approach 1: Plug in numbers that make the math easy.

If the number of copies of A = the number of copies of B, then p=50, since 1/2 of the newspapers sold are A.

If 4 copies of each type of newspaper are sold, then the total revenue will be an integer:
Revenue from 4 copies of A = 4*1 = 4.
Revenue from 4 copies of B = 4*1.25 = 5.
Total revenue = 4+5 = 9.

Since r% of the revenue comes from A:
r = revenue from A/total revenue * 100 = 4/9 * 100 = 400/9. This is our target.

Now we plug p=50 into the answers to see which yields our target of 400/9.
The denominator of the correct answer choice must yield a multiple of 9.
For an integer to be a multiple of 9, the sum of its digits must be a multiple of 9.
A quick scan of the denominators reveals that only D works:

125-p = 125-50 = 75. Not a multiple of 9.
250-p = 250-50 = 200. Not a multiple of 9.
375-p = 375-50 = 325. Not a multiple of 9.
500-p = 500-50 = 450, which is a multiple of 9.
625-p = 625-50 = 575. Not a multiple of 9.

The correct answer is D.

Approach 2: algebra

Let the number of newspapers sold = 100.
Since p% are A, the number of copies of A sold = p/100 * 100 = p.
Thus, the number of copies of B sold = 100-p.

Revenue from A = p*1 = p.
Revenue from B = (100-p)(1.25) = 125 - 1.25p.
Total revenue = p + (125 - 1.25p) = 125 - .25p.

Since r% of the total revenue comes from A:
r = revenue from A/total revenue * 100 = p/(125 - .25p) * 100 = 100p / (125 - .25p).

Since the answer choices do not include any decimals, we must clear .25 by multiplying by 4/4:
(100p)(4) / (125 - .25p)(4) = 400p/(500-p).

The correct answer is D.

[Brent@GMATPrepNow]

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 you're not sure how to proceed with this question, or if you're behind on time and you want to catch up, you can give yourself a 50-50 chance in about 10 seconds.

To do so, we'll see what happens when we use an extreme value for p.
Say p = 100
In other words, 100% of the newspapers sold were Newspaper A.
This means that 100% of the revenue is from Newspaper A.
In other words, when p = 100, then r = 100

At this point, we'll plug in 100 for p and see which one yields a value of 100.
Only answer choices B and D work.
B) 150(100)/(250-100) = 100 PERFECT
D) 400(100)/(500-100) = 100 PERFECT

Now take a guess (B or D) and move on.

Cheers,
Brent