Problem 79 - Elementary Algebra

Question

Problem: Complete the "Understand the problem," "Make a plan," and "Carry out the plan" steps for this problem: Find the percent of community college students nationwide who can attend college full-time. If students can attend full-time, they are four times as likely to complete as part-timers. But only 29 percent of California students can attend full-time. That's 12 percentage points below the national community college figure. (Source; www .communitycollegetimes.com, Aug. 3, 2007)

Step-by-Step Solution

Answer

41% of community college students nationwide can attend college full-time.

Step 1: Understand the Problem

The problem is to determine the percentage of community college students nationwide who can attend college full-time. We know that 29% of California students can attend full-time, and this is 12 percentage points below the national figure. We are asked to find this national percentage.

Step 2: Make a Plan

To find the national percentage of community college students who can attend full-time, add the number of percentage points that California is below the national average (12 percentage points) to the percentage of California students who can attend full-time (29%).

Step 3: Carry Out the Plan

Add the 12 percentage points to the 29% of California students who can attend full-time: \( 29\text{%} + 12\text{%} = 41\text{%} \). Therefore, 41% of community college students nationwide can attend full-time.

Key Concepts

percentages

Percentages are a way of expressing a number as a fraction of 100. They are widely used in various fields, including finance, statistics, and algebra, to simplify the comparison of ratios. In this problem, we deal with percentages to determine the proportion of community college students who can attend full-time.

Here are some key points to understand:

• A percentage is often denoted using the symbol %. For example, 29% means 29 out of 100.
• The concept of percentage points is crucial. When we say something is 12 percentage points below a figure, we mean we subtract 12 from that figure.
• In this exercise, we find a national percentage by adding the percentage difference (12%) to the percentage of California students attending full-time (29%).

Remember, understanding percentages will help you interpret data and perform algebraic calculations more effectively.

algebraic problem-solving

Algebraic problem-solving involves breaking down a problem into understandable steps and solving it using mathematical principles. The given problem can be broken down into three main steps: understanding the problem, making a plan, and carrying out the plan.

• First, we need to fully grasp what is being asked: finding the national percentage of community college students who can attend full-time.
• Next, we plan our approach. Here, we identify that adding the percentage difference (12%) to the given California percentage (29%) will give us the nationwide percentage.
• Lastly, we carry out our plan by performing the addition: \(29\text{\text{%}} + 12\text{\text{%}} = 41\text{\text{%}}\).

By following these structured steps, algebra helps to demystify complex problems and provides a clear path to the solution.

community college statistics

Community college statistics often include data on student attendance, completion rates, and other educational metrics. In the context of this exercise, we focus on the percentage of students attending full-time.

• These statistics help educators and policymakers understand trends and challenges within the community college system.
• In this example, only 29% of California community college students can attend full-time, compared to a 41% national average.
• Such statistics can inform decisions about resource allocation, student support programs, and policy changes to improve educational outcomes.

Understanding and analyzing community college statistics is essential for improving the quality and accessibility of education for all students.