Answer :
Answer:
The number of key rings sold on a particular day when the total profit is $5,000 is 4,000 rings.
Step-by-step explanation:
The question is incomplete.
An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by
[tex]P=n^2-2n-3[/tex]
where n is the number of key rings in thousands.
Find the number of key rings sold on a particular day when the total profit is $5,000.
We have the profit defined by a quadratic function.
We have to calculate n, for which the profit is $5,000.
[tex]P=n^2-2n-3=5\\\\n^2-2n-8=0[/tex]
We have to calculate the roots of the polynomial we use the quadratic equation:
[tex]n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\n= \frac{-2\pm\sqrt{4-4*1*(-8)}}{2}= \frac{-2\pm\sqrt{4-32}}{2} = \frac{-2\pm\sqrt{36}}{2} =\frac{-2\pm6}{2} \\\\n_1=(-2-6)/2=-8/2=-4\\\\n_2=(-2+6)/2=4/2=2[/tex]
n1 is not valid, as the amount of rings sold can not be negative.
Then, the solution is n=4 or 4,000 rings sold.