1. **State the problem:** A cashier scans 50 items in 10 minutes. We need to find how many minutes it takes to scan 32 items at the same rate. 2. **Formula and explanation:** The rate of scanning is constant, so we use the formula for unit rate: $$\text{Rate} = \frac{\text{Items}}{\text{Time}}$$ 3. **Calculate the rate:** $$\text{Rate} = \frac{50}{10} = 5 \text{ items per minute}$$ 4. **Find the time for 32 items:** Let $t$ be the time in minutes to scan 32 items. Using the rate formula: $$5 = \frac{32}{t}$$ 5. **Solve for $t$:** Multiply both sides by $t$: $$5t = 32$$ Divide both sides by 5: $$t = \frac{32}{5}$$ Show cancellation: $$t = \frac{\cancel{32}}{\cancel{5}} = 6.4$$ 6. **Answer:** It will take the cashier **6.4 minutes** to scan 32 items. Therefore, the correct choice is **A 6.4 min**.