Problem 12 - Prealgebra

Question

Solve each of the following problems by first restating it as one of the three basic percent problems of Section 7.2 . In each case, be sure to show the equation. According to the U.S. Census Bureau, national population estimates grouped by age and gender for july, \(2006,\) approximately \(7.4 \%\) of the \(147,512,152\) males in our population are between the ages of 15 and 19 years old. How many males are in this age group?

Step-by-Step Solution

Answer

Approximately 10,916,900 males are aged between 15 and 19 years.

Step 1: Understand the Problem

We know that we need to find the number of males aged between 15 and 19 years out of a total population of 147,512,152 males. We are given that 7.4% of these males fall into the 15-19 age group.

Step 2: Set Up the Percent Equation

We use the formula: Percentage × Total Male Population = Number of Males in the Age Group. Here, this corresponds to 7.4% of 147,512,152. We need to express 7.4% as a decimal for calculations.

Step 3: Convert Percentage to Decimal

To use 7.4% in a calculation, convert it to a decimal by dividing by 100. This gives us 0.074.

Step 4: Calculate the Number of Males

Multiply the decimal form of the percentage by the total number of males: \[ 0.074 \times 147,512,152 = 10,916,900 \] (approximately).

Step 5: Review and Interpret the Result

The calculation tells us approximately how many males aged 15 to 19 are there. Hence, about 10,916,900 males are between 15 and 19 years old in the given population.

Key Concepts

Understanding the Percent Equation

The percent equation is a fundamental tool used to solve various problems involving percentages. It's important because it connects the percentage, total amount, and the partial amount affected by the percentage. This equation can help decode many situations, from population statistics to financial applications. In its most basic form, the percent equation is expressed as:

• Percentage × Total = Part

For example, if we know that 7.4% of the male population is aged 15 to 19, we can set up the equation as: \[7.4\% \times 147,512,152 = \text{Number of Males in the Age Group}\]This formula allows you to solve for any unknown part of the equation when the other two values are given. For this particular problem, knowing the percentage and the total population gives us the number of males in the 15-19 age group.

Converting Percentage to Decimal Made Simple

Understanding how to convert a percentage into a decimal is vital when performing calculations like those in the percent equation. Percentages are essentially a fraction of 100, and converting them into decimals is a simple yet crucial step in this process. To convert any percentage to a decimal:

• Divide the percentage by 100.
• For example, converting 7.4% involves calculating \( \frac{7.4}{100} \).
• This gives a decimal result of 0.074.

By converting percentages to decimals, it simplifies multiplication. You can then multiply the decimal value by the total population to find out how many individuals are in the age group or category you are examining. In this exercise, using the decimal 0.074 allows you to multiply directly with the total number of males, streamlining the process to find that specific subgroup.

Insights Into Population Statistics

Population statistics are a powerful way to understand the demographic composition of a population, such as those provided by the U.S. Census Bureau. In the context of this exercise, statistics highlight the number of individuals within specific age brackets, giving us insights into population dynamics. For example, knowing that 7.4% of males fall into the 15 to 19 age category is crucial for planning educational resources, healthcare, and other age-specific policies. Understanding the age distribution helps governments and organizations plan for future needs:

• Helps in resource allocation, ensuring age groups are catered for appropriately.
• Provides data for social services planning and implementation.
• Offers insight into potential future economic and workforce trends based on age demographics.

This also assists in making informed decisions for community planning and development, thereby enhancing society's overall well-being. In summary, delving into population statistics offers a lens through which society can see and plan for its present and future needs.