If the equation on the board had shown 3 atoms of carbon on the reactants side, it would need 3 atoms of carbon on the product side to balance it.
This is in accordance to the law of conservation of mass which states that "matter is neither created nor destroyed during the course of chemical reaction, they are only transformed from one form to another".
We expect the same number of atoms on both sides of the equation. For example:
Fe + S → FeS
1 iron atom combines with 1 sulfur atom to produce FeS which contains 1 iron and sulfur atoms.