Problem 21 - Elementary Algebra

Question

Find the population of China a decade ago. Write the answer using the word million. For now, China remains the most populous nation, with \(1.34\) billion people. In the past decade it added \(73.9\) million, more than the population of France or Thailand. (Source: www.chicagotribune.com, Oct. 15, 2011)

Step-by-Step Solution

Answer

The population of China a decade ago was 1266.1 million.

Step 1: Understand the Problem

Determine the population of China ten years ago based on the current population and the population growth over the past decade.

Step 2: Identify Current Population

The current population of China is given as 1.34 billion people.

Step 3: Convert Billion to Million

Convert 1.34 billion people to million people. Since 1 billion is equivalent to 1000 million, this means 1.34 billion is equal to 1340 million.

Step 4: Subtract Population Growth

Subtract the population growth over the past decade, which is 73.9 million, from the current population in millions: \[1340 \text{ million} - 73.9 \text{ million} = 1266.1 \text{ million}\]

Step 5: State the Result

The population of China a decade ago was 1266.1 million.

Key Concepts

Basic Algebra

Basic algebra is vital in solving simple word problems like calculating population growth. In this exercise, you need to understand how to manipulate numbers and perform basic arithmetic operations to find the solution. Here, you use subtraction because you are reversing the population growth to find the past population. By subtracting the increase from the current population, you get the population from a decade ago. Algebra helps you to structure the problem and carry out the necessary steps in a logical order.

Unit Conversion

Understanding unit conversion is crucial, especially when dealing with large numbers. In this exercise, the population is given in billions, but we need to work in millions. Since 1 billion equals 1000 million, converting is straightforward. For example, to convert 1.34 billion into millions, multiply by 1000: \(1.34 * 1000 = 1340 \) million. This conversion helps you easily perform arithmetic operations because you're consistently using the same units throughout the problem.

Subtraction

Subtraction is an arithmetic operation you often need to solve word problems. To find the population of China a decade ago, you subtract the population growth of 73.9 million from the current population in millions (1340 million). This operation is written as: \[1340 \text{ million} - 73.9 \text{ million} = 1266.1 \text{ million} \] Subtraction helps to remove the additional amount added over the decade, giving you the original value from ten years ago. Therefore, the population of China a decade ago was 1266.1 million.