Problem 82 - Elementary Algebra

Question

It is estimated that \(8.3 \%\) of the total student population carpools to campus each day. If there are 13,000 students, then estimate the number of students that carpool to campus.

Step-by-Step Solution

Answer

About 1,079 students carpool to campus.

Step 1: Understanding the Problem

We need to find out how many students carpool to campus. The problem gives us the total number of students and the percentage of students who carpool.

Step 2: Write Down the Given Information

The total number of students is 13,000 and the percentage of students who carpool is 8.3%.

Step 3: Convert Percentage to Decimal

Convert 8.3% to a decimal for calculation. We do this by dividing by 100.\[ 8.3\% = \frac{8.3}{100} = 0.083 \]

Step 4: Calculate the Number of Students Who Carpool

Multiply the total number of students by the decimal form of the percentage: \[ 13,000 \times 0.083 = 1,079 \]

Step 5: Interpretation of Results

Approximately 1,079 students carpool to campus each day.

Key Concepts

Carpooling Estimation

Carpooling estimation involves understanding how many individuals in a group participate in carpooling. In our case, we're looking at the student population commuting to campus. To estimate how many students carpool, we need two key pieces of information:

• Total number of students
• Percentage of those students who carpool

With this data, we use percentage calculations to estimate how many students are likely to carpool. Estimating helps schools and local authorities plan for things like parking needs and transportation incentives. It's not an exact science but gives a useful approximation. It's as if you have a pie showing all the students, and you want to see just the slice that represents those who carpool. This slice is expressed as a percentage, and we calculate it using the total number of students.

Student Population

The term "student population" refers to all students enrolled at an institution. In this exercise, we have 13,000 students total. The student population forms the base number when calculating percentages for various activities like carpooling. Understanding the size of the student body is crucial when doing logistics and planning. Let's break this idea down:

• Imagine a big box with 13,000 marbles, each representing a student.
• We are interested in finding out how many of these marbles (students) are involved in specific activities, like carpooling.

The student population is the starting point for any percentage calculation because it tells us what 100% looks like before we zero in on the percentage of interest.

Decimal Conversion

Decimal conversion is a vital part of solving percentage problems. It allows us to use percentages in mathematical formulas. In our exercise, we needed to find out what 8.3% of 13,000 students is. First, we convert 8.3% into a decimal:

• Divide 8.3 by 100 to move the decimal two places left.
• This gives us 0.083.

This decimal is what you'll multiply by the student population to find the number who carpool. Why do we convert percentages to decimals? Think of percentages as being out of a hundred, but in calculations, they're easier handled as decimals. It's like translating the percentage into a language our calculation can "speak." Once you have your decimal, multiplication tells us how many parts out of the whole are of interest. This final step gives us an estimated count of carpoolers.