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Word Problems Involving Percent

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Word Problems Involving Percent

Study Guide

Key Definition

In percent problems, use the equation: $x \% \times y = z$

Important Notes

Identify the unknown variable: $x$, $y$, or $z$
Convert percent to a fraction: $\frac{x}{100}$
Use cross-multiplication for solving proportions
Remember: $\frac{part}{whole} = \frac{percent}{100}$
Check your solution by plugging values back into the equation

Mathematical Notation

$\times$ represents multiplication

$\div$ or $/$ represents division

$\% \text{ of }$ translates to $\times \frac{1}{100}$

Remember to use proper notation when solving problems

Why It Works

Percent problems use the relationship between parts and whole, expressed as $\frac{part}{whole} = \frac{percent}{100}$

Remember

Convert percent to decimal by dividing by 100: $x\% = \frac{x}{100}$

Quick Reference

Percent Formula:$\frac{part}{whole} = \frac{percent}{100}$

Understanding Word Problems Involving Percent

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To find what percent a part is of the whole, divide the part by the whole and then multiply by 100. For example, $(165 ÷ 200) × 100 = 82.5\%$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What percent of $200$ is $165$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A can of soda is $75\%$ full and weighs $150$ grams. What was the original weight when full?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A store sells items at $20\%$ discount. If an item originally costs $\$50$, what is the sale price?

Challenge Quiz

Single Choice Quiz

Advanced

If $z$ is $30\%$ of $y$ and $y = 150$, find $z$.

Recap

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Review key concepts and takeaways