Question

18.) A relationship between the number of a certain AA battery packs x,that a store sells each day and the price p per battery pack is givenby the equation: x = 1400 - 100p. At what prices p should the packsof batteries be sold for the daily revenue R to be $4500?Use: R= xp(12 pts)9

Answer 1

$5 and $9

Explanation:

We have that the relationship between the battery pack and the price per battery would be:

`x=1400-100p`

And the equation of the daily revenue is:

`R=x\cdot p`

We replace the first equation in the second and we obtain:

`R=(1400-100p)\cdot p`

We replace the value of R and solve for p, so we can know the prices

`\begin{gathered} 4500=1400p-100p^2 \\ -100p^2+1400p-4500=0 \\ -100\cdot(p^2-14p+45)=0 \\ p^2-14p+45=0 \\ (p-5)\cdot(p-9)=0 \\ p-5=0\rightarrow p=5 \\ p-9=0\rightarrow p=9 \end{gathered}`

That is, when the price is $5 and $9, there is a revenue of $4500