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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.

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Answer:

[tex]\mathbf{r = \dfrac{400p }{ 500 -p}}[/tex]

Step-by-step 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 ;

[tex]r = \dfrac{A}{A+1.25B} \times 100[/tex]  --- (1)

[tex]p = \dfrac{A}{A+B} \times 100[/tex]        --- (2)

From (2)

[tex]A+B = \dfrac{A}{p} \times 100[/tex]

[tex]B = \dfrac{A}{p} \times 100-A[/tex]

[tex]B = \dfrac{A( 100-p)}{p}[/tex]

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

[tex]r = \dfrac{A}{A+1.25 \times { \dfrac{A( 100-p)}{p}}} \times 100[/tex]

[tex]r = \dfrac{A}{A+1.25 \times { A( 100-p)}} \times 100p[/tex]

[tex]r = \dfrac{100p}{p+125 -1.25 p}[/tex]

[tex]r = \dfrac{100p}{125 -0.25 p}[/tex]

multiplying both numerator and denominator by 4; we have

[tex]r = \dfrac{4(100p) }{ 4(125 -0.25) p}[/tex]

[tex]\mathbf{r = \dfrac{400p }{ 500 -p}}[/tex]

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