What is the simplest formula for the mineral beryl which contains 5.03% Be, 10.4% Al, 35.5% Si and 53.58% O?
Firstly the "correct" answer seems to be wrong, which is not an uncommon occurrence, so please do not always take answers at the back of books to be correct. Wikipedia lists the formula of beryl as $\ce{Be3Al2(SiO3)6}$ which is much more in accordance with what you have done.

That aside, there are two things you need to correct.


The percentages that you have in your first step are different from those quoted in the title. For example, for silicon, you divided 31.35 by 32, but the title says that there is 35.5% silicon. Please, be more careful when you are pressing numbers into a calculator or the computer. The same issue exists for aluminium and oxygen.
In your second step, oxygen, you seem to have done a calculation pertaining to the first step? You meant to do 3.3/0.558, correct?


Fix those and you should obtain the correct answer - and not the one in the back of whatever text you are using.