**Category:** Organic Chemistry  
**Subtype:** Chemical Reactions (Acid-Base Reactions)  
**Problem Description:** This problem involves a reaction between an amino acid mixture and hydrochloric acid (HCl) to form salts. The task is to determine the amount of HCl (in moles) that reacted with the given mass of the amino acid mixture, based on the mass of the resulting salt produced.  

**Key Points:**  
- You have a mixture of two amino acids: \(\mathrm{CH}_{3}-\mathrm{CH}\left(\mathrm{NH}_{2}\right)-\mathrm{COOH}\) (which is alanine) and \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{CH}_{2}-\mathrm{COOH}\) (which is glycine).  
- The total mass of the amino acid mixture is 4.78 grams.  
- The reaction with HCl produces 6.97 grams of salt.  
- You need to find the value of \(a\), the number of moles of HCl that reacted.  

This problem requires knowledge of stoichiometry and the ability to relate mass and moles in chemical reactions.