Question
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A checkout clerk at a department store completed 6 transactions in 20 minutes. Select all the rates that apply. \( \frac{6 \text { minutes }}{20 \text { transactions }} \) \( 3 \frac{1}{3} \) minutes per transaction \( \frac{20 \text { minutes }}{6 \text { transactions }} \) \( \frac{3}{5} \) transaction per minute 0.3 transaction per minute \( \frac{6 \text { transactions }}{20 \text { minutes }} \)

Ask by Wheeler Bolton. in the United States
Jan 24,2025

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Tutor-Verified Answer

Answer

The applicable rates are: - 3 1⁄3 minutes per transaction - 20 minutes per 6 transactions - 0.3 transaction per minute - 6 transactions per 20 minutes

Solution

To determine which rates apply to the scenario where a checkout clerk completed **6 transactions in 20 minutes**, let's analyze each option: 1. **\( \frac{6 \text{ minutes}}{20 \text{ transactions }} \)** - **Analysis:** This implies that **6 minutes** were spent on **20 transactions**, which contradicts the given scenario where **20 minutes** were spent on **6 transactions**. - **Conclusion:** **Not applicable.** 2. **\( 3 \frac{1}{3} \) minutes per transaction** - **Calculation:** \( \frac{20 \text{ minutes}}{6 \text{ transactions}} = \frac{20}{6} \approx 3.333 \) minutes per transaction. - **Conclusion:** **Applicable.** 3. **\( \frac{20 \text{ minutes}}{6 \text{ transactions }} \)** - **Calculation:** Directly represents the rate of minutes per transaction. - **Conclusion:** **Applicable.** 4. **\( \frac{3}{5} \) transaction per minute** - **Calculation:** \( \frac{6 \text{ transactions}}{20 \text{ minutes}} = 0.3 \) transactions per minute, not \( \frac{3}{5} \) (which is 0.6). - **Conclusion:** **Not applicable.** 5. **0.3 transaction per minute** - **Calculation:** \( \frac{6 \text{ transactions}}{20 \text{ minutes}} = 0.3 \) transactions per minute. - **Conclusion:** **Applicable.** 6. **\( \frac{6 \text{ transactions }}{20 \text{ minutes }} \)** - **Calculation:** Directly represents the rate of transactions per minute. - **Conclusion:** **Applicable.** **Therefore, the applicable rates are:** - \( 3 \frac{1}{3} \) minutes per transaction - \( \frac{20 \text{ minutes}}{6 \text{ transactions }} \) - 0.3 transaction per minute - \( \frac{6 \text{ transactions }}{20 \text{ minutes }} \) **Final Selection:** - \( 3 \frac{1}{3} \) minutes per transaction - \( \frac{20 \text{ minutes}}{6 \text{ transactions }} \) - 0.3 transaction per minute - \( \frac{6 \text{ transactions }}{20 \text{ minutes }} \)

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Bonus Knowledge

One of the fun facts about rates is that they help us understand how things change over time! For the checkout clerk, knowing how fast they’re processing transactions can lead to better customer service. So, the rate of \( \frac{6 \text{ transactions}}{20 \text{ minutes}} \) shows that they're serving customers at a steady pace, approximately 0.3 transactions per minute. To optimize performance, the clerk could work on improving their speed to handle more transactions in the same time frame. For instance, if they could reduce the time per transaction to about 3 minutes and 20 seconds, they’d notch up productivity. Juggling efficiency while maintaining customer satisfaction is key – let's keep those lines moving smoothly!

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