You find a compound composed only of element "X" and hydrogen, and know that it is 91.26% element X by mass. Each molecule has 2.67 times as many H atoms as X atoms. What is element X?

Since you know the ratio of atoms, you can start to put a formula togeter. The formula might look like:

X H2.67

but since atoms can't come in fractional amounts, we have to multiply the formula by some number in order to turn 2.67 into a whole #, while still maintaining the ratio. Multiplying 2.67 by 3 yields 8, so the most likely ratio in the molecule is

X3H8 so the ratio of 1:2.67 is still maintained. The mass percent tells you that out of every 100g of compound, 91.26g is element X, so the other 8.74g must be H. Dividing each mass by the number of moles in the formula gets us the molar mass of each element (approximately). DIviding 8.74g by 8 gets 1.09, roughly the molar mass of hydrogen. Dividing 91.26g by 3 gets us 30.4, roughly the molar mass of phosphorus. Element X is most likely phosphorus