Problem 57 - Algebra A Combined Function

Question

A recent survey showed that \(42 \%\) of recent college graduates named flexible hours as their most desired employment benefit. In a graduating class of 860 college students, how many would you expect to rank flexible hours as their top priority in job benefits? (Round to the nearest whole.) (Source: JobTrak.com)

Step-by-Step Solution

Answer

About 361 students would prioritize flexible hours.

Step 1: Understand the Problem

First, we need to comprehend the scenario. We know that 42% of college graduates prefer flexible hours as their top employment benefit. We also have a total of 860 students to consider. Our task is to determine how many students would prefer flexible hours.

Step 2: Set Up the Calculation

To find the number of students who desire flexible hours, we'll calculate 42% of 860. The percentage can be expressed as a decimal for calculation purposes: 42% = 0.42.

Step 3: Perform the Calculation

Multiply the total number of students (860) by the decimal representation of the percentage (0.42) to find the expected number of students:\[ 860 imes 0.42 = 361.2 \]

Step 4: Round the Result

Since the problem asks for an answer rounded to the nearest whole number, we round 361.2 to 361. Therefore, approximately 361 students would rank flexible hours as their top priority.

Key Concepts

Decimal Conversion

When working with percentages, it's often useful to convert them into a decimal form to simplify calculations. This process, known as decimal conversion, involves dividing the percentage by 100. For example, in our problem, we need to convert 42% into a decimal. To do this, simply divide 42 by 100, which gives us 0.42.

• Percent to Decimal: Divide by 100
• Example: 42% becomes 0.42

This conversion is crucial because it allows for straightforward calculations involving multiplication with other numbers, like figuring out how many students prefer flexible hours. Always remember, when you see a percentage, picture it over 100 and then handle it as a decimal in your calculations.

Multiplication of Percentages

After converting a percentage into a decimal, the next step in solving such problems is multiplying the decimal by another number, often a total quantity. This helps determine the portion or amount related to the percentage. For instance, in the given exercise where we have 860 students, we need to find out 42% of this total. Once converted, 42% is 0.42. Next, we take this decimal and multiply it by the total number of students.\[ 860 \times 0.42 = 361.2 \]This result signifies the expected number of graduates who would rank flexible hours as their top job benefit priority. Multiplication of percentages as decimals allows for easy computation of parts of a whole.

Rounding Numbers

Rounding numbers is a useful skill, especially when a problem requires the answer in whole numbers. The process involves adjusting a number up or down to the nearest whole number based on the decimal part. Let's revisit the example from our initial exercise. After calculating, we end up with 361.2 students. Since this isn't a feasible number of people, we need to round it. Here's a quick guide:

• Look at the digit after the decimal point.
• If it's 5 or more, round up.
• If it's less than 5, round down.

In our problem, since 0.2 is less than 5, we round 361.2 down to 361. Thus, approximately 361 students would prioritize flexible hours, which makes it easy to report results in a practical, usable way.