Problem 44 - Algebra 1

Question

The 267.9 million people in the United States consumed 639.4 million kilograms of the cocoa produced in the \(1996-1997\) growing year. Which choice better represents the amount of cocoa consumed per person that year? Explain. \(.\) Source: International Cocoa Organization A. 2.38671146 kilograms B. about 2.4 kilograms

Step-by-Step Solution

Answer

Choice B: about 2.4 kilograms, is a better representation of the amount of cocoa consumed per person that year. It is a rounded version of the exact value and is easier to understand and apply in most contexts.

Step 1: Understand the Problem

This problem involves calculating the per capita cocoa consumption.

Step 2: Calculate Per Capita Consumption

To find the per capita consumption, we will divide the total quantity of cocoa by the total population. The formula for this is: \[\frac{{\text{{total kilograms of cocoa consumed}}}}{{\text{{total population}}}}\] Inserting the given data, we will compute \[\frac{{639.4 \times 10^6 \text{{ kg}}}}{{267.9 \times 10^6 \text{{ people}}}}.\]

Step 3: Compute the Division

By computing the division, we'll get approximately 2.38671146 kg of cocoa per person.

Step 4: Compare the Result to Given Choices

Now we will compare our result with the two provided choices. Choice A is exact, but for general use and easy understanding, we may prefer rounded figures. Looking at choice B, about 2.4 kilograms, we can see it is a rounded version of our calculated result and also an easier number to comprehend.

Key Concepts

Per Capita Consumption

When we talk about "per capita consumption," we refer to the average amount of a specific commodity consumed by each individual in a given population. This concept is crucial in fields like economics and public health to analyze and compare consumption across different regions or countries. To find per capita consumption, you need two pieces of information:

• Total quantity consumed
• Total population

The computation involves dividing the total amount of a commodity by the population size. For example, in our cocoa consumption problem, we have a total of 639.4 million kilograms of cocoa consumed in the U.S. by 267.9 million people. By dividing these two values, we determine how much cocoa each person, on average, consumed during the specified period. It's a simple yet effective way to distill large-scale data into a more comprehensible form.

Division

Division is a basic arithmetic operation that is used to split a total amount into equal parts. It's the operation we used to find per capita consumption. For instance, when you divide 639.4 million kilograms of cocoa by the 267.9 million people, you effectively determine how much each individual, on average, consumes. The formula is straightforward:

• Numerator: the total amount (639.4 million kg)
• Denominator: the total population (267.9 million people)

Once you perform the division, the result you obtain is a precise figure representing the per capita consumption. In our example, that result is approximately 2.38671146 kilograms per person. Understanding division helps us break down totals into meaningful, digestible insights, such as our calculation for cocoa consumption.

Rounding Numbers

Rounding numbers is the process of simplifying a number while keeping its value close to what it originally was. It's particularly useful when you want to present data in a way that's easier to understand and communicate, for instance, in reports or quick summaries. In mathematics, we often round numbers to a certain decimal place to make them more practical.
When rounding the calculated cocoa consumption of 2.38671146 kilograms per person, you might round it to one decimal place, resulting in 2.4 kilograms. This is done by observing the next digit (8 in this case), which is more than 5, and increasing the preceding digit by 1. Therefore, option B, which states about 2.4 kilograms, represents our rounded number. Choosing rounded numbers provides clarity, reduces complexity, and helps people remember and discuss figures more conveniently.