Question

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 revenue from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of Newspaper B. Write an expression in terms of r and p.

Answer 1

`\mathbf{r = (400p )/( 500 -p)}`

Explanation:

Given that:

Last Sunday a certain store sold copies of Newspaper A for $1.00 each

A = 1

and copies of Newspaper B for $1.25 each,

B = 1.25

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 B.

Then ;

`r = (A)/(A+1.25B) * 100` --- (1)

`p = (A)/(A+B) * 100` --- (2)

From (2)

`A+B = (A)/(p) * 100`

`B = (A)/(p) * 100-A`

`B = (A( 100-p))/(p)`

Substituting the value of B into equation (1), we have:

`r = \frac{A}{A+1.25 * { (A( 100-p))/(p)}} * 100`

`r = \frac{A}{A+1.25 * { A( 100-p)}} * 100p`

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

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

multiplying both numerator and denominator by 4; we have

`r = (4(100p) )/( 4(125 -0.25) p)`

`\mathbf{r = (400p )/( 500 -p)}`