Problem 74 - Elementary Algebra

Question

A survey of 325 people who intended to travel on the Memorial Day weekend in 2011 found that three-fifths said that rising gasoline prices would not affect their travel plans. Find the number of surveyed people who said that rising gasoline prices would not affect their travel plans. (Source: www.aaanewsroom.net, May 2011)

Step-by-Step Solution

Answer

195 people

Step 1: Understand the problem

A survey of 325 people found that three-fifths of them said rising gasoline prices would not affect their travel plans. The goal is to find out how many people said the prices would not affect their plans.

Step 2: Identify the fraction

The fraction of people who said that rising gasoline prices would not affect their travel plans is three-fifths, which can be written as the fraction \(\frac{3}{5}\).

Step 3: Set up the calculation

Use the total number of people surveyed, which is 325, and multiply it by the fraction found in Step 2. This gives the expression: \(325 \times \frac{3}{5}\).

Step 4: Perform the multiplication

Calculate the product: \(325 \times \frac{3}{5} = 325 \times 0.6 = 195\).

Step 5: Interpret the result

The result of the multiplication is 195, which means 195 people said that rising gasoline prices would not affect their travel plans.

Key Concepts

Fraction Multiplication

Fraction multiplication is a fundamental concept in elementary algebra. It is used to determine a part of a whole. In our example, the problem involves finding a fraction of a total number of people surveyed. Knowing how to multiply fractions is essential for solving such problems successfully.

To multiply a fraction by a whole number, follow these steps:

• Convert the whole number to a fraction by putting it over 1. For example, 325 becomes \(\frac{325}{1}\).
• Multiply the numerators (top numbers) of the fractions
• Multiply the denominators (bottom numbers) of the fractions
• Simplify the resulting fraction if possible

Applying this process to our exercise, where three-fifths (\(\frac{3}{5}\)) of 325 people were surveyed about their travel plans, we set up the multiplication \(\frac{3}{5} \times 325\)\

Survey Analysis

Survey analysis is the process of understanding and interpreting the data collected from a survey. Surveys are a great tool in collecting information and understanding trends among a specific population.

In our example, the survey involved 325 people, and the key question was how rising gasoline prices affected their travel plans. From this data, we learned that three-fifths of the respondents felt unaffected by the price change.

Here’s a step-by-step guide to analyze such survey data:

• Understand the size of your sample. In this case, it's 325 respondents
• Identify the key data points. For us, it's the fraction (three-fifths) who said prices wouldn’t affect them
• Convert this information into meaningful numbers by using arithmetic operations like multiplication
  
  The goal of survey analysis is to gain insights from the data collected and draw meaningful conclusions. It helps in decision-making and understanding trends and behaviors within a given population.

Word Problems in Math

Word problems in math can seem intimidating, but they are simply real-life scenarios needing mathematical solutions. These problems help develop critical thinking and problem-solving skills.

In word problems, always follow these steps:

• Read the problem carefully and understand what’s being asked
• Identify key numbers and operations needed to solve the problem (e.g., ‘three-fifths’, ‘325 people’)
• Set up an equation that represents the problem
• Solve the equation step by step
• Interpret the result within the context of the problem

In our example, the word problem asked how many people (out of 325) indicated that rising gasoline prices wouldn’t affect their travel plans. By identifying the numbers and operations involved, we set up a fraction multiplication problem (\(\frac{3}{5} \times 325\)), solved it, and concluded that 195 people remain unaffected.

By breaking down word problems into these manageable steps, students can approach them with confidence and ease.