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
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.
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