A 1.0-ounce piece of chocolate contains 15 mg of caffeine, and a 6.0-ounce cup of regular coffee contains 105 mg of caffeine. How much chocolate would you have to consume to get as much caffeine as you would from 2.0 cups of coffee?

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Determine the total amount of caffeine in 2.0 cups of coffee by multiplying the caffeine content of one cup by 2.

Calculate the total caffeine content in 2.0 cups of coffee: $ 105 \, \text{mg/cup} \times 2 \, \text{cups} $.

Set up a proportion to find out how many ounces of chocolate are needed to match the caffeine content of 2.0 cups of coffee.

Use the proportion: $ \frac{15 \, \text{mg}}{1.0 \, \text{oz}} = \frac{\text{Total caffeine from 2.0 cups of coffee}}{x \, \text{oz of chocolate}} $.

Solve the proportion for $ x $ to find the number of ounces of chocolate needed.

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Key Concepts

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

Caffeine Content Calculation

To determine how much caffeine is in a specific amount of chocolate, one must understand the concentration of caffeine in the chocolate. In this case, 1.0 ounce of chocolate contains 15 mg of caffeine, which allows for straightforward calculations to find the total caffeine content in larger quantities of chocolate.

Unit Conversion

Unit conversion is essential for comparing different quantities. In this question, converting ounces of chocolate to milligrams of caffeine and cups of coffee to milligrams of caffeine is necessary to find an equivalent amount of caffeine from chocolate that matches the caffeine intake from coffee.

Proportional Relationships

Understanding proportional relationships helps in solving the problem by establishing a ratio between the caffeine content in chocolate and coffee. By knowing the caffeine content per unit of each substance, one can set up a proportion to find the required amount of chocolate to match the caffeine from 2.0 cups of coffee.

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