Problem 88 - Elementary Algebra

Question

A group of military veterans that took a survey included 134 women and 577 men. Find the percent of the group who were women. Round to the nearest percent. (Source: www.pewsocialtrends.org, Dec. 22, 2011)

Step-by-Step Solution

Answer

19%

Step 1: Identify Total Number of Veterans

First, determine the total number of veterans surveyed by adding the number of women and men. Total veterans = number of women + number of men Total veterans = 134 + 577

Step 2: Calculate Total Number of Veterans

Add the numbers to get the total. Total veterans = 134 + 577 = 711

Step 3: Find Proportion of Women in the Group

Next, find what proportion of the group are women by dividing the number of women by the total number of veterans. Proportion of women = \(\frac{134}{711}\)

Step 4: Convert Proportion to Percent

Convert the proportion to a percent by multiplying by 100. Percentage of women = \(\frac{134}{711} \times 100\)

Step 5: Round to Nearest Percent

Calculate and round the result to the nearest percent. Percentage of women = \(18.85\text{ which rounds to 19}\) Therefore, the percentage of the group who were women is roughly 19%.

Key Concepts

percentages

Understanding percentages is crucial in many real-world applications. In simpler terms, a percentage is a way of expressing a number as a fraction of 100. If you have 19 out of 100 parts, you have 19 percent.

To convert a fraction to a percentage, like in the given exercise, you multiply the fraction by 100. Here, the fraction of women in the group is \(\frac{134}{711}\). To find the percentage, multiply this fraction by 100: \(\frac{134}{711} \times 100\).

This gives approximately 18.85 which rounds to 19. Therefore, 19% of the group are women.

proportions

A proportion is simply a part, share, or number considered in comparative relation to a whole. In the exercise, the proportion refers to the part of the group that consists of women.

To find this, you divide the number of women by the total number of veterans. So, if there are 134 women and 711 total veterans, the proportion of women is \(\frac{134}{711}\).

This means that for every 711 veterans, there are 134 who are women. Proportions help us compare parts of a total without getting confused by the actual numbers.

basic arithmetic

Basic arithmetic skills are foundational for solving problems like this one. Addition enables us to find the total number of veterans by summing the number of men and women.

In this case, the sum is \({134 + 577 = 711}\). Once we have the total, we use division for finding the proportion: \(\frac{134}{711}\).

Finally, multiplication and understanding rounding help convert the proportion to a percentage: \(\frac{134}{711} \times 100 = 18.85\) which rounds to 19.

Mastering these basic operations makes complex problems approachable and solvable.