Problem 29 - Elementary Algebra

Question

If \(15 \%\) of the area of a park is playground and the area of the park is 6 acres, find the area of the playground.

Step-by-Step Solution

Answer

0.90 acres

Step 1: Understand the Problem

We need to find the area of the playground, knowing it is 15% of the total park area, which is 6 acres.

Step 2: Convert Percentage to Decimal

Convert 15% to a decimal by dividing by 100. \( 15\text{\textpercent} = \frac{15}{100} = 0.15 \)

Step 3: Multiply the Decimal by the Total Area

To find 15% of the park's area, multiply the decimal (0.15) by the total area (6 acres). \( 0.15 \times 6 = 0.90 \)

Step 4: Write the Final Answer

The area of the playground is 0.90 acres.

Key Concepts

percentage calculations

Percentage calculations are fundamental in many areas of math and real-life applications. To solve these problems, it's essential to understand that a percentage represents a part of a whole.

Percentages are out of 100, meaning that 15% is the same as saying 15 out of 100.

In this specific exercise, we are trying to find out what 15% of 6 acres is. The first step is to convert the percentage to a decimal, making calculations easier.

decimal conversion

Converting percentages to decimals is simple.

Just divide the percentage by 100. For example, 15% becomes 0.15 when we divide 15 by 100:

\[ \frac{15}{100} = 0.15 \]

Decimals are easier to work with in multiplication and most other arithmetic operations.

multiplication of decimals

Once we have the decimal form of the percentage, we can easily find the desired portion of the total area. In this case, the decimal form 0.15 needs to be multiplied by the total park area of 6 acres:

\[ 0.15 \times 6 = 0.9 \]

This multiplication gives you the area of the playground. Therefore, 0.9 acres of the park is used as a playground.
In conclusion, the steps to solve this type of percentage problem involve:

• Converting the percentage to a decimal
• Multiplying the decimal by the total

Following these steps ensures accurate results and a clear understanding of percentage calculations.