1. **State the problem:** Alice has $a$ chocolates and Bob has $b$ chocolates. Alice gives half of her chocolates to Bob. Then Bob gives half of all the chocolates he now has to Alice. We want to find how many chocolates Alice has at the end, in terms of $a$ and $b$. 2. **Step 1: Alice gives half her chocolates to Bob.** - Alice gives away $\frac{a}{2}$ chocolates. - Alice now has $a - \frac{a}{2} = \frac{a}{2}$ chocolates. - Bob receives $\frac{a}{2}$ chocolates, so Bob now has $b + \frac{a}{2}$ chocolates. 3. **Step 2: Bob gives half of his chocolates to Alice.** - Bob has $b + \frac{a}{2}$ chocolates. - Half of this is $\frac{1}{2} \left(b + \frac{a}{2}\right) = \frac{b}{2} + \frac{a}{4}$. - Bob gives this amount to Alice. 4. **Step 3: Calculate Alice's final chocolates.** - Alice had $\frac{a}{2}$ chocolates after step 1. - She receives $\frac{b}{2} + \frac{a}{4}$ from Bob. - Total chocolates Alice has now: $$\frac{a}{2} + \frac{b}{2} + \frac{a}{4} = \frac{2a}{4} + \frac{2b}{4} + \frac{a}{4} = \frac{3a}{4} + \frac{b}{2}$$ **Final answer:** Alice now has $$\boxed{\frac{3a}{4} + \frac{b}{2}}$$ chocolates. This means Alice ends up with three-quarters of her original chocolates plus half of Bob's original chocolates.