60. Solving a chemistry problem

47. The drug lekrolin eye drops contains benzalkonium chloride as one of the substances, which consists of three components, conventionally designated as C12, C14, and C16. The regulated content of benzalkonium chloride is 0.04 mg/ml.
The content of benzalkonium chloride in lecrolin is determined by HPLC with an external standard according to the peak areas of the C12, C14, and C16 components on the chromatograms of the test and standard solutions.
To prepare the test solution, mix 1 ml of lecrolin with 1 ml of a diluent (a mixture of water and 2-propanol in a volume ratio of 35:65). Get the test solution.
To prepare a standard solution, dilute 1 ml of a 10% solution of pure benzalkonium chloride (standard sample 100 mg in 1 g of solution) with water to 100 ml. Transfer 2 ml of the resulting solution into a 50 ml volumetric flask and bring the volume of the solution in the flask to the mark with a mixture of acetonitrile: 2-propanol: HClO4 solution (pH=2.2) in a volume ratio of 18:25:57. Get a standard solution. The HPLC chromatograph is used to chromatograph the test and standard solutions, measure the peak areas of the C12, C14, and C16 components in both chromatograms, and calculate the content of benzalkonium chloride in lecrolin in mg/ml.
Derive the formula for calculating the content m(X) of benzalkonium chloride in the original drug lecrolin in mg/ml, if SC12x, SC14x, and SC16x are, respectively, the peak areas of the components C12, C14, and C16 on the chromatogram of the test solution; SC12st, SC14st, and SC16st are, respectively, the content of components C12, C14, and C16 (in mg/ml) in the standard solution.
Calculate the content of benzalkonium chloride (mg/ml) in the standard solution.