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Recall that you can solve a percent problem by translating the words into an equation where the percent is written as a decimal. Example: What percent of 20 is 5 ? Translates as \( 5=20 x \) \( x=0.25 \), or \( 25 \% \) Example: What is \( 40 \% \) of 20 ? Translates as \( x=0.4(20) \) \( x=8 \)

Ask by Grant Barber. in the United States
Jan 30,2025

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To solve a percent problem, translate the words into an equation where the percent is written as a decimal. For example, "What percent of 20 is 5?" translates to \(5 = 20 \times x\), and solving for \(x\) gives \(x = 0.25\) or \(25\%\). Similarly, "What is 40% of 20?" translates to \(x = 0.4 \times 20\), resulting in \(x = 8\).

Solution

Let's break down the process of solving percent problems step by step, using the examples you've provided as a guide. ### Example 1: What percent of 20 is 5? 1. **Translate the words into an equation**: - We want to find what percent \( x \) of 20 is equal to 5. This can be expressed as: \[ 5 = 20 \cdot x \] 2. **Solve for \( x \)**: - To isolate \( x \), divide both sides by 20: \[ x = \frac{5}{20} \] 3. **Calculate \( x \)**: - Simplifying the fraction: \[ x = 0.25 \] 4. **Convert to a percentage**: - To convert \( x \) to a percentage, multiply by 100: \[ x = 0.25 \cdot 100 = 25\% \] ### Example 2: What is \( 40\% \) of 20? 1. **Translate the words into an equation**: - We want to find \( x \) which is \( 40\% \) of 20. This can be expressed as: \[ x = 0.4 \cdot 20 \] 2. **Calculate \( x \)**: - Performing the multiplication: \[ x = 8 \] ### Summary of Steps: - For "What percent of \( A \) is \( B \)?", use the equation \( B = A \cdot x \). - For "What is \( C\% \) of \( A \)?", use the equation \( x = \frac{C}{100} \cdot A \). If you have a specific percent problem you'd like to solve, please provide the details, and I can help you work through it!

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Mind Expander

Did you know that the concept of percentages has roots dating back to ancient civilizations? The term "percent" originates from the Latin "per centum," meaning "by the hundred." Ancient Romans used this principle in trade and taxation, which helped lay the foundation for the modern financial systems we use today. Understanding percentages is truly a timeless skill! In the real world, percentages are everywhere, from calculating discounts during sales to figuring out tip amounts at restaurants! When a store advertises "20% off," it’s a percentage problem in disguise. If you want to know how much you're saving on that adorable pair of shoes marked at $50, just use \( 0.20 \times 50 \) to calculate your savings of $10, making that charming footwear a steal at $40!

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