To find the jacket prices that will make the store exactly $12,000 in revenue, we need to set up an equation using the given expression for the number of jackets sold (-2p + 320) and the revenue goal ($12,000).

The revenue is calculated by multiplying the price of each jacket (p) by the number of jackets sold (-2p + 320). So, we set up the equation as follows:

p(-2p + 320) = 12,000

Expanding this gives:

-2p^2 + 320p = 12,000

Rearranging the terms to one side gives a quadratic equation:

2p^2 - 320p + 12,000 = 0

We can solve this quadratic equation for p (the price of the jackets) using the quadratic formula:

p = [320 ± sqrt((320)^2 - 4*2*12000)] / (2*2)

Calculating the values gives:

p = [320 ± sqrt(102400 - 48000)] / 4

p = [320 ± sqrt(54400)] / 4

p = [320 ± 233.238] / 4

So, the two possible prices for the jackets that will make the store exactly $12,000 in revenue are:

p = (320 + 233.238) / 4 = $138.81

and

p = (320 - 233.238) / 4 = $21.69.

Question

To find the jacket prices that will make the store exactly $12,000 in revenue, we need to set up an equation using the given expression for the number of jackets sold (-2p + 320) and the revenue goal ($12,000).

The revenue is calculated by multiplying the price of each jacket (p) by the number of jackets sold (-2p + 320). So, we set up the equation as follows:

p(-2p + 320) = 12,000

Expanding this gives:

-2p^2 + 320p = 12,000

Rearranging the terms to one side gives a quadratic equation:

2p^2 - 320p + 12,000 = 0

We can solve this quadratic equation for p (the price of the jackets) using the quadratic formula:

p = [320 ± sqrt((320)^2 - 4*2*12000)] / (2*2)

Calculating the values gives:

p = [320 ± sqrt(102400 - 48000)] / 4

p = [320 ± sqrt(54400)] / 4

p = [320 ± 233.238] / 4

So, the two possible prices for the jackets that will make the store exactly $12,000 in revenue are:

p = (320 + 233.238) / 4 = $138.81

and

p = (320 - 233.238) / 4 = $21.69.

Knowee AI · Accepted Answer