Step 1: The nucleus of an atom is made up of two kinds of particles, protons and neutrons, which are together called nucleons.
Step 2: The mass number, denoted A, is defined as the total count of protons plus neutrons in the nucleus, because these two particles carry almost all the mass of the atom while electrons contribute negligibly to mass.
Step 3: The number of protons alone is called the atomic number, not the mass number, so option A is incorrect. The number of protons and electrons being equal only describes a neutral atom's charge balance, it is not what mass number means, so option B is incorrect. The number of neutrons alone is only part of the mass, since protons also contribute, so option D is incorrect.
Step 4: Since mass number equals number of protons plus number of neutrons, which equals the total number of nucleons, the correct answer is option C.