Problem 32 - Elementary Algebra

Question

Find the percent of episodes of drinking and driving in 2010 for which men were responsible. Men were responsible for 4 in 5 episodes ... of drinking and driving in 2010. (Source: www.cdc.gov, Oct. 2011)

Step-by-Step Solution

Answer

Men were responsible for 80% of episodes of drinking and driving in 2010.

Step 1: Identify the given information

According to the problem, men were responsible for 4 out of 5 episodes of drinking and driving in 2010.

Step 2: Understand the meaning of '4 in 5'

'4 in 5' means that in every 5 episodes of drinking and driving, men were responsible for 4 of those episodes.

Step 3: Convert the fraction to a percentage

To find the percentage, we'll convert the fraction \(\frac{4}{5}\) to a percent by multiplying by 100.\[ \frac{4}{5} \times 100 = 80 \text{ percent} \]

Key Concepts

Fractions to Percents

Understanding how to convert fractions to percents is essential. We use it frequently in real-life scenarios, like in this exercise about drinking and driving statistics. To convert a fraction to a percent:

• First, recognize the fraction form. Here, we have \(\frac{4}{5}\) which represents 4 out of 5.
• Next, multiply the fraction by 100. This step converts the fraction into a percent form. So, \[ \frac{4}{5} \times 100 = 80\text{%} \]

This means that men were responsible for 80% of drinking and driving episodes. Converting fractions to percents is simple and only involves basic multiplication!

Drinking and Driving Statistics

Understanding statistics is crucial for grasping the depth of real-world problems. Here we explore drinking and driving. In 2010, men were responsible for a significant proportion of these incidents. Specifically:

• 4 in 5 episodes were caused by men.
• Which translates to 80 out of every 100 episodes.

Such statistics highlight the need for targeted education and interventions. By diving into these numbers, we can better understand where to focus efforts to reduce incidents.

Algebra Problem-Solving Steps

Algebra is a cornerstone of math that helps solve real-world problems. Here, we break down a percent calculation involving algebra. Follow these steps:

• Step 1: Identify the given information. We start by noting that men were responsible for 4 out of 5 episodes.
• Step 2: Understand the fraction '4 in 5'. This fraction represents a part of a whole.
• Step 3: Convert the fraction to a percent. Multiply \(\frac{4}{5} \) by 100 to get the result, which is 80%.

By following these steps systematically, any student can handle algebra problems more confidently.