Problem 20 - Prealgebra

Question

Solve each problem using the percent equation. 27 is \(54 \%\) of what number?

Step-by-Step Solution

Answer

27 is 54% of 50.

Step 1: Write the Percent Equation

The percent equation is given by the formula: \( \text{Part} = (\text{Percent} \times \text{Whole}) \). In this problem, 27 is the part, 54% is the percent, and the unknown number is the whole.

Step 2: Convert the Percent to Decimal

To use the percent in the equation, convert it to a decimal by dividing by 100. So, \(54\%\) becomes \(0.54\).

Step 3: Substitute Known Values into the Equation

Substitute the known values into the equation: \( 27 = 0.54 \times \text{Whole} \).

Step 4: Solve for the Whole

To find the value of the whole, divide both sides of the equation by \(0.54\): \( \text{Whole} = \frac{27}{0.54} \).

Step 5: Calculate the Result

Perform the division to find the whole number: \( \text{Whole} = \frac{27}{0.54} \approx 50 \).

Key Concepts

Converting Percentages to Decimals

When you're working with percentages in equations, it's crucial to convert them into decimals. This process simplifies calculations and helps maintain consistency in mathematical expressions. Here's how you do it:

• Take the percentage value, in this case, 54%.
• Divide the percentage by 100 to convert it into a decimal. So, 54% becomes 0.54.

This conversion is based on the fact that a percentage is essentially a fraction out of 100. Dividing by 100 shifts the decimal point two places to the left, making it easier to work with.
For example, 75% becomes 0.75, and 150% becomes 1.50 when converted to decimals. Always remember, changing a percentage to a decimal is the first step when adopting the percent equation method.

Solving Equations

Solving equations is a fundamental skill in mathematics. To solve for an unknown variable, you need to isolate it using standard algebraic techniques. In the context of our exercise, we start with the equation:

• 27 = 0.54 × Whole

Our goal is to solve for the 'Whole,' or what number 27 is 54% of. We achieve this by:
1. Dividing both sides of the equation by 0.54. This operation helps isolate the 'Whole' on one side of the equation.
2. Conducting the division 27 ÷ 0.54 using a calculator or long division.
Once completed, you find that the 'Whole' equals approximately 50. This solution shows how breaking down the equation helps find the answer efficiently.

Pre-Algebra Problem-Solving

Pre-algebra problem-solving is about applying basic mathematical concepts to solve real-world problems. Percent equations are a part of this, helping us understand relationships between numbers.
In our previous example, we determined a 'Part' (27) as a percentage (54%) of a 'Whole' (unknown). This typical pre-algebra problem involves:

• Identifying key components of the problem: part, whole, and percentage.
• Using algebraic operations to simplify and solve equations.

The essence of pre-algebra is to take complex scenarios and break them down into solvable steps. By practicing these skills, you build a strong mathematical foundation crucial for understanding more advanced concepts. Using these techniques regularly will make tackling numerical problems less intimidating and more intuitive.