Problem 13 - 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. Bachelors According to the U.S. Census Bureau data for the number of marriages in 2004 approximately \(31.2 \%\) of the \(109,830,000\) males age 15 years or older have never been married. How many males age 15 years or older have never been married?

Step-by-Step Solution

Answer

34,261,296 males have never been married.

Step 1: Understand the Problem

We need to find the number of males aged 15 years or older who have never been married based on a given percentage. We have a total of 109,830,000 males and 31.2% of them have never been married.

Step 2: Restate as a Percent Problem

We need to find a certain percentage of a given total. This is a typical percent problem where we are given the percentage and the total, and we need to find the part corresponding to the percentage. The equation to use is: \[ \text{Part} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total} \]

Step 3: Plug Values into Equation

Substitute the given values into the equation: percentage \( = 31.2\) and total number of males \( = 109,830,000\). Thus, the equation becomes: \[ \text{Part} = \left( \frac{31.2}{100} \right) \times 109,830,000 \]

Step 4: Calculate the Solution

Perform the calculation: \(\frac{31.2}{100} = 0.312\). Then multiply: \[ 0.312 \times 109,830,000 = 34,261,296 \] males.

Step 5: State the Final Answer

The number of males aged 15 years or older who have never been married is 34,261,296.

Key Concepts

Percentage Calculation

Understanding percentage calculation is crucial in everyday mathematics. When solving percent problems, we usually want to find a part of a total based on a given percentage. This involves three key elements:

• **Total**: The overall quantity. In our problem, it's the total number of males aged 15 years or older.
• **Percentage**: The rate or proportion given. Here, it's the percentage of males who have never been married, 31.2%.
• **Part**: The quantity that represents the percentage of the total. This is what we solve for.

To find the part, we use the formula:\[\text{Part} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total}.\]This equation is straightforward. First, you convert the percentage into a decimal by dividing by 100. Then, multiply that decimal by the total amount to find the desired part. For instance, in our problem, 31.2% becomes 0.312 when divided by 100. Then multiplying by the total number of males gives us the number of males who have never been married.

Mathematical Equations

Mathematical equations help us represent real-world problems in a solvable format. In percentage problems, such as the one given, the equation reflects the relationship between the total, percentage, and part. With the equation:\[\text{Part} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total},\]we are setting up a simple multiplication problem to find our unknown - in this case, the part of the population never married.

Breaking down the equation:

• **Convert the percentage**: To transform 31.2% into usable form, divide by 100 to get 0.312.
• **Input the total**: Use the given number '109,830,000' as the total population of males 15 years or older.
• **Solve the equation**: Multiply 0.312 by 109,830,000 to find the number of unmarried males.

Mathematical equations like this one simplify complex operations into manageable calculations, making them an essential tool in quantitative reasoning.

U.S. Census Data Analysis

The U.S. Census Bureau collects vast amounts of data, which are critical in understanding demographic trends and patterns. Data analysis of such information can reveal significant details about societal behaviors and needs. In analyzing the census data about unmarried males:

• **Data Collection**: The data is gathered from surveys and records, providing an expansive view of the population.
• **Percentage Analysis**: This part is crucial as it helps determine what proportion of a group displays a particular characteristic, such as being unmarried.
• **Decision Making**: Policymakers and researchers use this data to make informed decisions that can influence social and economic strategies.

In 2004, knowing that 31.2% of males aged 15 and older were unmarried provided insight into marriage trends. Such data helps predict future changes and address potential challenges, like planning for social services or understanding marriage rates' impact on the economy.