Question

Last Sunday a certain store sold copies of 256 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 revenue 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))`

Answer 1

D.
`(400p)/(500-p)`

Explanation:

let's call A the number of copies sold of newspaper A and B the number of copies sold of newspaper B.

So, we can formulate the following equations from the sentence: a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each as:

A + B = 256 (1)

1A + 1.25 B = Total Revenue (2)

Then, r and p are equal to:

`r=(A)/(Total Revenue)*100=(100A)/(A+1.25B)` (3)

`p=(A)/(256) *100=(100A)/(256)` (4)

Isolating A from (4) and B from (1), we get:

`A=(256p)/(100) =2.56p` (5)

`B=256-A=256-2.56p` (6)

Finally, replacing (5) and (6) in (3), we get:

`r=(100A)/(A+1.25B)=(100(2.56p))/(2.56p+1.25(256-2.56p))\\\\r=(256p)/(2.56p+320-3.2p)=(256p)/(320-0.64p)\\\\r=(256p/0.64)/((320-0.64p)/0.64)=(400p)/(500-p)`