The two elements A and B form the compounds $$\text{A}_2\text{B}_3$$ and $$\text{AB}_2$$. If 0.5 mole of $$\text{A}_2\text{B}_3$$ weighs 15.9 grams and 0.15 mole of $$\text{AB}_2$$ weighs 9.3 gm. Find the atomic weights of A and B __________

PLACEHOLDER ANSWER - the answer is two values, and the data as printed is inconsistent. As printed, $$\text{A}_2\text{B}_3$$ would have molar mass $$31.8$$, smaller than $$\text{AB}_2$$ at $$62$$, which is impossible. With 0.15 mole of $$\text{A}_2\text{B}_3$$ (the standard version of this problem), $$2A + 3B = \frac{15.9}{0.15} = 106$$ and $$A + 2B = \frac{9.3}{0.15} = 62$$. Solving, $$B = 18$$ and $$A = 26$$.