A company that manufactures hair ribbons knows that the number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation below. x = 1,000 − 100p
At what price should the company sell the ribbons if it wants the weekly revenue to be $1,600? (Remember: The equation for revenue is R = xp.)
p = $ (smaller value)
p = $ (larger value)

Given:

The number of ribbons it can sell each week, x, is related to the price p per ribbon by the equation:

To find:

The selling price if the company wants the weekly revenue to be $1,600.

Solution:

We know that the revenue is the product of quantity and price.

We need to find the value of p when the value of R is $1600.

Divide both sides by 100.

Splitting the middle term, we get

Using zero product property, we get

or

or

Therefore, the smaller value of p is $2 and the larger value of p is $8.

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