Problem 36 - Algebra 1: Concepts and Skills

Question

The 267.9 million people in the United States consumed 639.4 million kilograms of cocoa produced in the 1996–1997 growing year. Which choice better represents the amount of cocoa consumed per person that year? Explain your reasoning. $$A. 2.38671146 kilograms$$ $$B. about 2.4 kilograms$$

Step-by-Step Solution

Answer

The choice that better represents the amount of cocoa consumed per person in the year 1996-1997 is about 2.4 kilograms. Despite being a rounded value, it is still a close approximation to the precise amount and is more suitable for practical purposes.

Step 1: Identify the problem

The task here is to identify which of the two numbers better represents the average cocoa consumption per person in a given year. The two numbers given are 2.38671146 kilograms and about 2.4 kilograms.

Step 2: Calculate the average cocoa consumption

To calculate the average cocoa consumption per person, divide the total cocoa consumed by the total population. Doing this calculation: 639.4 million kilograms / 267.9 million people, results in an average of 2.38671146 kilograms per person.

Step 3: Discuss precision and appropriateness

While 2.38671146 is the more accurate number, it has too many decimal places for practical use. Not only is it more challenging to remember and use, but the level of precision is unnecessary in the context of average cocoa consumption per person. On the other hand, 2.4 kilograms (having rounded the number to one decimal place) is easier to remember and use, and is precise enough for this context. Therefore, 2.4 kilograms is the choice that better represents the amount of cocoa consumed per person that year.

Key Concepts

Cocoa Consumption

Cocoa consumption refers to the total amount of cocoa used or eaten by a specific group of people, whether in a city, country, or globally. Understanding cocoa consumption can provide insights into dietary preferences, economic implications, and cultural practices. In the United States, cocoa is used in various forms, such as in chocolate, baked goods, and beverages.

• The importance of tracking cocoa consumption lies in its impact on economies and health.
• Consumption data helps businesses make decisions about production and marketing.
• It influences policies on agriculture and trade.

Calculating cocoa consumption per person can aid in understanding how frequently and in what quantities cocoa-related products are enjoyed by individuals.

Per Capita Calculation

Per capita calculation is a method used to find the average amount per person in a population for a given total. It involves dividing the total quantity of something by the number of people in the group. In our exercise, we need to determine the average cocoa consumption per person in the United States.
To perform this:

• Divide the total cocoa consumed (639.4 million kilograms) by the total population (267.9 million people).

This results in an average of approximately 2.38671146 kilograms of cocoa consumed per person. Using per capita calculations can help in comparing how resources or products are distributed among different populations. It provides a clearer perspective on individual usage rather than just looking at aggregate totals.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify numbers, making them easier to understand and use. It involves adjusting a number to a specified degree of precision, which can vary depending on the context. In the context of our exercise, rounding is important for clarity and ease of communication. For example, the exact figure for cocoa consumption per capita is 2.38671146 kilograms. However, this number has many decimal places, which can be cumbersome and unnecessary for day-to-day use.

• To round to one decimal place, observe the digit in the second decimal place.
• If it's 5 or more, increase the first decimal by one. Otherwise, leave it.

Thus, 2.38671146 rounds to 2.4 kilograms when rounded to one decimal place. Using this rounded figure, it becomes more straightforward to communicate and comprehend, particularly in general discussions.