Question

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

Answer 1

Option 400p/500-p

Explanation:

Let the number of newspaper A sold be 'x'

and the number of newspaper A sold be 'y'

Therefore,

Total revenue = $1x + $1.25y

Total newspapers sold = x + y

Therefore,

according to the question

r =
`(x)/(x + 1.25y)*100` ..........(1)

and,

p =
`(x)/(x + y)*100`

or

(x + y)p = 100x

or

y =
`(x)/(p)*100-x`

or

y =
`(x(100-p))/(p)`

substituting y in 1

r =
`(x)/(x + 1.25((x(100-p))/(p)))*100`

or

r =
`(100p)/(p+125-1.25p)`

or

r =
`(100p)/(125-0.25p)`

multiply and divide the RHS with 4

we get

r = (400p)÷(500-p)

hence,

Option 400p/500-p