Problem 4 - Algebra 1: Concepts and Skills

Question

Write an equation for each question. Do not solve the equation. 99 is what percent of 212?

Step-by-Step Solution

Answer

The equation is \(Percentage = \frac{99}{212} * 100%.\)

Step 1: Identify the Whole and the Part

From the problem, the 'Whole' is 212 and the 'Part' is 99.

Step 2: Formulate the Percentage Equation

Formulate the equation using the general percentage equation \(Percentage = \frac{Part}{Whole} * 100\%. Replace 'Part' with 99 and 'Whole' with 212. The equation becomes \(Percentage = \frac{99}{212} * 100%.\)

Key Concepts

Understanding Percentage Equations

Percentage equations are a powerful tool for expressing the relationship between two numbers. They let us understand how one value (the part) compares to another value (the whole), in terms of percent. Typically, percentage equations follow the formula \(Percentage = \frac{Part}{Whole} \times 100\%\). Here’s how it works:

• "Part" is the portion or the amount of interest.
• "Whole" is the total or full amount.
• The equation gives us what percent the "Part" is of the "Whole" by dividing the two and then multiplying by 100 to convert the fraction to a percentage.

Using this equation helps streamline problem solving where percentages are involved. It simplifies the comparison between the two values into a clear, understandable percentage form. This method applies across different fields and situations, such as finances or statistics.

Whole and Part Identification

Before creating a percentage equation, it's important to correctly identify the whole and the part in the problem statement. Think of the "Whole" as the total set you are dealing with. It's usually the larger quantity compared to the part. In contrast, the "Part" is the smaller subset or portion you need to measure against the whole. In our original exercise, we look at two numbers: 212 and 99. Here:

• The "Whole" amount referred to was 212.
• The "Part" in question was 99.

This simple step is indispensable because mixing up these values can lead to incorrect equations and misinterpretations of the data. Always double-check which number represents the total and which one is merely a portion of it before proceeding to the next steps in solving percentage problems. This ensures your results will be reliable and accurate.

Formulating Equations for Percent Problems

Formulating equations is a critical step when solving problems involving percentages. Once you've identified your part and whole, it's time to plug these into the percentage formula. The foundational equation, \(Percentage = \frac{Part}{Whole} \times 100\%\), guides this process effectively.When approaching our example:

• We substitute "Part" with 99.
• We plug "Whole" with 212.

By putting these values into the formula, the equation becomes \(Percentage = \frac{99}{212} \times 100\%\). This equation allows you to find out what percentage 99 is of 212 without any further complicated calculations beyond these basic substitution steps.Formulating the equation in this manner provides a straightforward path to express complex relationships in simple numerical terms. Moreover, this method aids in efficiently tackling a wide array of similar percentage-based challenges you might encounter.