Problem 31 - Prealgebra

Question

A national survey of 6700 teens was conducted, and it found that \(81 \%\) of teens between the ages of 12 and 17 use the Internet to e-mail friends or relatives. About how many teens in the survey was this?

Step-by-Step Solution

Answer

5427 teens use the Internet to email.

Step 1: Understanding the Problem

We need to find out how many teens from the survey used the Internet to email friends or relatives. We know that 81% of the 6700 teens surveyed used the internet in this way.

Step 2: Set Up the Calculation

To find the actual number of teens, we need to calculate 81% of 6700.

Step 3: Convert Percentage to Decimal

To calculate 81% as a decimal, divide by 100. So, 81% becomes 0.81.

Step 4: Calculate the Number

Multiply the total number of teens, 6700, by the decimal 0.81: \( 6700 \times 0.81 \).

Step 5: Perform the Multiplication

Calculate the product: \( 6700 \times 0.81 = 5427 \).

Step 6: Conclude the Answer

Thus, 5427 teens in the survey use the Internet to email friends or relatives.

Key Concepts

Understanding Proportions in Percentage Calculations

In order to solve problems involving percentages, it's crucial to grasp the concept of proportions. When we see a percentage, it represents a part of a whole; more specifically, it tells us how many parts out of 100 we are dealing with. In our problem, we know that 81% of the teens in a survey used the internet to email friends or family. This implies we're talking about 81 out of every 100 teens involved in the survey.

• To solve for the specific number of teens using the internet, we treat the entire group of 6700 teens as our 'whole', or 100%.
• Thus, to find out how many teens equate to 81% of this total, we need to work out what 81 out of every 100 teens would correspond to if we had 6700 "units" of teens in total.

The power of proportions allows us to translate these percentages into actionable numbers by first understanding them conceptually before proceeding with numerical calculations.

Decimal Conversion of Percentages

Handling percentages within equations often requires us to convert these figures to decimals, as calculators and algebraic operations frequently depend on decimal rather than percentage format. The conversion process is simple and involves a basic rule: divide the percentage by 100.

• This converts a percentage like 81% into a decimal, which becomes 0.81.
• This conversion helps us perform multiplication directly without needing to adjust units manually.

By understanding decimal conversion, we streamline our calculations when solving percentage problems, making it a fundamental aspect of solving real-world mathematical queries.

Step-by-Step Problem Solving Approach

Successfully solving percentage problems often depends on following a clear, step-by-step methodology. This systematic approach ensures that you don't miss anything crucial. In our example, we followed these steps:

• Understand the Problem: Identify what information is provided and what you need to find out.
• Set Up the Calculation: Clearly state what you need to calculate—in this case, 81% of 6700.
• Perform Required Conversions: Convert percentages to decimals (81% = 0.81) to simplify calculations.
• Calculate: Multiply the total number of units (teens) by the decimal representing the percentage (6700 × 0.81).
• Conclude: Interpret the calculated result in the context of the original problem.

Using such structured problem-solving steps not only aids in tackling percentage problems effectively; it can also be applied to numerous mathematical problems to enhance understanding and accuracy.