Problem 14 - 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. Bachelorettes According to the U.S. Census Bureau data for the number of marriages in \(2004,\) approximately \(25.8 \%\) of the \(117,677,000\) females age 15 years or older have never been married. How many females age 15 years or older have never been married?

Step-by-Step Solution

Answer

Approximately 30,366,666 females aged 15 or older have never been married.

Step 1: Understand the Problem

First, identify what is being asked in the problem. We need to find out how many females aged 15 years or older have never been married.

Step 2: Identify the Total Quantity

The total number of females aged 15 or older is given as 117,677,000. This represents the whole or 100% of the population in this context.

Step 3: Determine the Percentage

According to the problem, 25.8% of these females have never been married. This is the percentage required to calculate the specific part of the total population.

Step 4: Set Up the Percentage Equation

To find the number of females who have never been married, use the equation: \[\text{Number of never married females} = (\text{Percentage}) \times (\text{Total females})\]Substitute the values into the equation: \[\text{Number of never married females} = 0.258 \times 117,677,000\]

Step 5: Calculate the Result

Perform the multiplication to find the number of never-married females. \[0.258 \times 117,677,000 = 30,366,666\]Thus, approximately 30,366,666 females aged 15 years or older have never been married.

Key Concepts

Percentage Calculation

Understanding percentage calculation is important when dealing with problems that ask for a part of a whole. In our exercise, we are asked to find out how many never-married females are among all females aged 15 or older. Here, the percentage helps us identify the portion of the total number.
To calculate this percentage, you need to follow a straightforward formula:- Identify the total quantity, which represents 100% of the whole.
- Determine the percentage of the whole you are interested in.
- Apply the percentage calculation formula: \[ \text{Part} = (\text{Percentage as a decimal}) \times (\text{Total quantity}) \]In our example, the percentage given is 25.8%. We first convert this percentage into a decimal by dividing by 100, resulting in 0.258.
Then, we multiply by the total number of 117,677,000 females. This calculation tells us how many females have never been married.
It's a practical way to find specific quantities within larger groups based on given percentages.

Problem Solving Steps

A structured approach to solving percentage problems involves several clear steps. By systematically working through these steps, we can ensure accuracy and understanding. Here is a breakdown of the necessary steps:- **Understand the Problem**: Clearly identify what the question is asking. In our scenario, the objective is to determine how many females have never been married.
- **Identify the Total Quantity**: Recognize what number represents the entire group. In this exercise, it is the 117,677,000 females aged 15 and older.- **Determine the Percentage**: Find the specific percentage you need to apply to the total. This tells us what portion of the total number we are interested in. Here, it is 25.8%.- **Set Up the Equation**: Be precise in setting up the mathematical equation. Use the formula \[ \text{Part} = (\text{Percentage}) \times (\text{Total}) \]- **Calculate the Result**: Perform the calculation using basic arithmetic to find the desired part of the population. By carefully following these steps, we simplify the problem into manageable pieces, making it much easier to solve.

Mathematical Equation

In problems involving percentages, setting up the correct mathematical equation is pivotal. The equation combines all necessary components and lays them out clearly.To solve our example problem, you will rely on the following equation: \[ \text{Number of never married females} = (\text{Percentage as a decimal}) \times (\text{Total number of females}) \]Here's how you should approach setting up this equation: - Convert the percentage from a percentage point to a decimal by dividing by 100. For example, 25.8% becomes 0.258.
- Plug in the percentage and the total number of the population into the equation.
- Multiply these numbers to solve for the part.
This setup helps ensure that each aspect of the problem is captured in the equation. By carefully constructing and solving it, you find the answer: 30,366,666 females aged 15 and older who have never been married. This crucial step simplifies complex problems into straightforward calculations.