Problem 77 - Elementary Algebra

Question

Find the number of \(2,200,000\) adults who binge drink about four times a month. Round to the nearest thousand. Binge drinking is a nationwide problem and bigger than previously thought. One in six adults binge drinks about four times a month. Binge drinking is defined as consuming four or more drinks for women or five or more drinks for men over a short period of time. Most binge drinkers are not alcohol-dependent. (Source: www.cdc.gov, Jan. 2012)

Step-by-Step Solution

Answer

367,000

Step 1 - Understand the Problem

Identify that we need to find the number of adults who binge drink monthly based on given statistics.

Step 2 - Identify Given Values

The problem states that 1 in 6 adults binge drinks about four times a month.

Step 3 - Set Up the Calculation

To find the number of binge drinkers, we use the ratio 1 in 6. This means \( \frac{1}{6} \) of the adult population binge drinks.

Step 4 - Perform the Calculation

Multiply the total number of adults, \(2,200,000\), by the ratio of binge drinkers: \( \frac{1}{6} \).\[ \frac{2,200,000}{6} = 366,666.67 \]

Step 5 - Round to the Nearest Thousand

Round 366,666.67 to the nearest thousand. The result is 367,000.

Key Concepts

binge drinking definition

Binge drinking is more common than you might think. But what exactly is it? According to the Centers for Disease Control and Prevention (CDC), binge drinking is defined based on the number of drinks consumed in a short time. For women, this means drinking 4 or more alcoholic beverages in a single session. For men, it’s 5 or more drinks.
Many binge drinkers engage in this behavior regularly, about four times a month. However, most binge drinkers are not alcohol-dependent, meaning they don't necessarily rely on alcohol every day.
Understanding this definition is crucial because it helps identify the magnitude of the problem. It is also essential for calculating the number of people affected by binge drinking in a given population.

ratio calculation

When tackling problems involving ratios, it's important to understand what a ratio represents. A ratio compares two quantities to show how much larger one quantity is compared to another. In this exercise, we are given the ratio of adults who binge drink: 1 in 6.
This means for every 6 adults, 1 of them binge drinks. To calculate the number of binge drinkers in a given population, we express this ratio as a fraction. Hence, the ratio 1 in 6 translates to \( \frac{1}{6} \).
If the total number of adults is 2,200,000, we multiply this by the ratio fraction to find the number of binge drinkers:
\r\[ \frac{2,200,000}{6} = 366,666.67 \]. This step ensures we accurately represent the part of the population that is binge drinking.

rounding to the nearest thousand

Rounding numbers makes them easier to work with, especially when dealing with large figures. In this exercise, after calculating the number of binge drinkers as \(366,666.67\), the next step is to round this number to the nearest thousand.
When rounding to the nearest thousand, we look at the hundreds digit (the third digit from the right). If this digit is 5 or higher, we round up. If it is 4 or lower, we round down.
For \(366,666.67\), the hundreds digit is 6. Since this is 5 or higher, we round up to the nearest thousand, resulting in 367,000.
This process ensures our final number is more manageable and easy to understand while still being an accurate representation of the data.