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?

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.