Answer :
Given: The profit function below
[tex]\begin{gathered} f(x)=x^2-14x+485 \\ f(x)=profit \\ x=Number-of-items \end{gathered}[/tex]To Determine: The number of items if the profit is $500
Solution
Substitute the value of the profit into the function
[tex]\begin{gathered} f(x)=500 \\ 500=x^2-14x+485 \\ x^2-14x+485-500=0 \\ x^2-14x-15=0 \end{gathered}[/tex][tex]\begin{gathered} x^2-15x+x-15=0 \\ x(x-15)+1(x-15)=0 \\ (x-15)(x+1)=0 \\ x-15=0,OR,x+1=0 \\ x=15,OR,x=-1 \end{gathered}[/tex]Since the number of items cannot be negative,
Hence, the number of items sold is 15