Step 1 :The elasticity function is given by \(E(x)=\frac{22 x}{711-22 x}\).
Step 2 :To find the price at which the elasticity of demand is equal to 1, we need to solve the equation \(E(x)=1\) for \(x\). This gives us the equation \(\frac{22 x}{711-22 x}=1\).
Step 3 :Solving this equation gives us \(x = \frac{711}{44}\).
Step 4 :However, the question asks for the answer to be rounded to the nearest cent. So, we round \(x\) to get the final price.
Step 5 :Final Answer: The price at which the elasticity of demand is equal to 1 is \(\boxed{16.16}\) cents.