When do mole amounts become whole-number coefficients?

An aluminium chloride process uses 5.40 g of aluminium and 21.3 g of chlorine gas to make 26.7 g of aluminium chloride, AlCl₃. Relative atomic masses are Al = 27 and Cl = 35.5. Use the masses to determine the balanced equation involving Al, Cl₂ and AlCl₃, and explain how the mole amounts lead to the coefficients.