(d) When the coffee is brewed according to directions, a pound of coffee beans yields 50 cups of coffee (4 cups = 1 qt). How many kg of coffee are required to produce 200 cups of coffee?

Verified step by step guidance

Start by determining how many pounds of coffee are needed to produce 200 cups. Since 1 pound yields 50 cups, divide 200 cups by 50 cups per pound to find the number of pounds needed.

Convert the number of pounds of coffee to kilograms. Use the conversion factor: 1 pound = 0.453592 kilograms.

Multiply the number of pounds by the conversion factor to get the mass in kilograms.

Ensure that all units are correctly converted and consistent throughout the calculation.

Review the steps to confirm that the logic and conversions are correct, ensuring the final answer is in kilograms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Conversion between units

Understanding how to convert between different units of measurement is essential in chemistry. In this question, we need to convert cups to pounds and then to kilograms. Knowing that 4 cups equal 1 quart helps in determining the total volume of coffee needed, while recognizing the conversion factor between pounds and kilograms (1 pound = 0.453592 kg) is crucial for the final calculation.

Proportional relationships

Proportional relationships allow us to determine how quantities relate to one another. In this scenario, we know that 1 pound of coffee beans yields 50 cups of coffee. By establishing this ratio, we can set up a proportion to find out how much coffee is needed for 200 cups, which involves scaling the amount of coffee beans based on the desired number of cups.

Dimensional analysis

Dimensional analysis is a systematic method used to convert one unit of measurement to another. It involves using conversion factors to cancel out units and arrive at the desired measurement. In this problem, dimensional analysis will help us navigate from cups of coffee to pounds of coffee beans and finally to kilograms, ensuring that all units are correctly accounted for throughout the calculation.