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

_{3}Y

_{2} because if a is 3 then b is 2.

but the answer in the book is X

_{2}Y

_{3}Maybe I'm missing something obvious...? or book is wrong