1. **State the problem.** Alan spent $\frac{7}{10}$ of his allowance on food, then spent half of what was left on stationery, and he had $3$ left. We need to find Alan’s original allowance and draw a ruler-style diagram. 2. **Set up the formula.** Let the total allowance be $x$. After food, the remaining amount is: $$x-\frac{7}{10}x=\frac{3}{10}x$$ After stationery, he had half of that remaining amount left: $$\frac{1}{2}\cdot\frac{3}{10}x=3$$ 3. **Solve the equation.** $$\frac{3}{20}x=3$$ Now divide both sides by $\frac{3}{20}$: $$x=3\div\frac{3}{20}$$ $$x=3\cdot\frac{20}{3}$$ $$x=20$$ Since we divided by a fraction, the cancellation is: $$\frac{\cancel{3}}{\cancel{20}}x=\cancel{3}$$ 4. **Check the answer.** Food: $$\frac{7}{10}\cdot 20=14$$ Remaining after food: $$20-14=6$$ Stationery: $$\frac{1}{2}\cdot 6=3$$ So the final amount left is $3$, which matches the problem. 5. **Final answer.** Alan’s original allowance was $20$.