I have recently stumbled upon a question I can't seem to solve :
Chlorine can also be used to synthesise a bromine-containing oxoanion that is mainly used in continuous or batch dyeing processes. When chlorine is passed through an aqueous solution containing potassium hydroxide and potassium bromide, the bromide ions are oxidised to the bromine-containing oxoanion. Careful addition of aqueous lead nitrate to the resulting solution precipitates 4.17g of $PbCl_2$. When this precipitate is filtered off and the resulting filtrate is evaporated, 0.835g of a white crystalline solid is obtained. The white solid has the following composition by mass : $K$, 23.4%; $Br$, 47.8%; $O$, 28.8%. $\mathbb \ Determine\ the\ formula\ of\ the\ white\ crystalline\ solid.$
I attempted by first finding the empirical formula of the solid using by dividing the percentage compositions by their respective elements' mass number, and ended up getting $KBrO_3$ as the empirical formula, which would make my second step to find $n$, where the molecular formula of the white crystalline solid is $K_nBr_nO_{3n}$. However, how can I go about doing this without being given how many moles of the white crystalline solid was precipitated? I can't seem to construct the equations that could potentially lead me to the mole ratio between $PbCl_2$ and $K_nBr_nO_{3n}$. If possible, can anyone tell me how to get a better grip on forming equations in scenarios such as this? I have been struggling in this topic for a while and this is likely to be one of the key reasons why. Sorry for the lengthy question!