I've worked through this problem but the back of the book has a different answer than the one I have.
The problem: A compound of X and Y is 1/3 X by mass. The atomic mass of element X is 1/3 the atomic mass of element Y. Find the empirical formula of the compound.
My work:Xa / (Xa + Yb) = 1/3
X = 1/3Y
(1/3Y)a/((1/3Y)a + Yb) = 1/3
1/3Ya = 1/3 (1/3Ya + Yb)
1/3Ya = 1/9Ya + 1/3Yb
1/3a = 1/9a + 1/3b
2/9a = 1/3b
6/9a = b
2/3a = b
Therefore the empirical formula is X
3Y
2 because if a is 3 then b is 2.
but the answer in the book is X
2Y
3Maybe I'm missing something obvious...? or book is wrong