Question

The yearly sales for a clothing storefrom 2015 can be modeled by thefunction f(x)=x²-14x + 485, wheref(x) represents profit and x representsthe number of items sold. How manyitems must the clothing store sell inorder to have a profit of $500?

Answer 1

Given: The profit function below

`\begin{gathered} f(x)=x^2-14x+485 \\ f(x)=profit \\ x=Number-of-items \end{gathered}`

To Determine: The number of items if the profit is $500

Solution

Substitute the value of the profit into the function

`\begin{gathered} f(x)=500 \\ 500=x^2-14x+485 \\ x^2-14x+485-500=0 \\ x^2-14x-15=0 \end{gathered}`
`\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}`

Since the number of items cannot be negative,

Hence, the number of items sold is 15