Solve and check the linear equation. \[ 27-\frac{x}{4}=\frac{x}{5} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an integer or a simplified fraction.) B. The solution set is $\{x \mid x$ is a real number $\}$. C. The solution set is $\varnothing$.

Step 1 ：Multiply every term by 20 to get rid of the fractions: \(20(27-\frac{x}{4})=20(\frac{x}{5})\), which simplifies to \(540-5x=4x\).

Step 2 ：Move all terms involving x to one side and constant terms to the other side: \(540=9x\).

Step 3 ：Simplify the equation and solve for x: \(x=\frac{540}{9}=60\).

Step 4 ：Check the solution by substituting x = 60 back into the original equation: \(27-\frac{60}{4}=\frac{60}{5}\), which simplifies to \(27-15=12\), and since both sides of the equation are equal, the solution is correct.

Step 5 ：Final Answer: The solution set is \(\boxed{60}\).