percentage system of equation word problem examples

Guri Bee

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20-10-2024

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Mastering Percentage Word Problems: A Step-by-Step Guide

Percentages are a fundamental part of everyday life. From understanding sales discounts to calculating interest rates, the ability to solve percentage word problems is a valuable skill. This article explores various types of percentage word problems with practical examples, providing a clear and concise approach to tackling them.

What are Percentage Word Problems?

Percentage word problems involve translating real-life scenarios into mathematical equations using the concept of percentages. These problems can range from simple calculations to complex scenarios with multiple variables.

Understanding the Basics:

What is a Percentage?

A percentage represents a part out of one hundred. The symbol "%" is used to denote percentage. For example, 50% means 50 out of every 100, which is equivalent to 0.50 in decimal form.

Key Formula:

The fundamental formula for solving percentage problems is:

Percentage = (Part / Whole) * 100

This formula can be rearranged to find the "Part" or the "Whole" if the other two values are known.

Common Types of Percentage Word Problems:

1. Finding a Percentage of a Number:

Problem: A store offers a 20% discount on a $100 item. How much is the discount?

Solution:

• Identify the "Whole": The original price of the item, $100.
• Identify the "Percentage": The discount, 20%.
• Apply the formula: Discount = (20 / 100) * $100 = $20

2. Finding the Whole When the Percentage and Part are Known:

Problem: A student scored 75% on a test. If the test had 40 questions, how many questions did the student answer correctly?

Solution:

• Identify the "Percentage": The student's score, 75%.
• Identify the "Part": The total questions on the test, 40.
• Rearrange the formula: Whole = (Part / Percentage) * 100
• Solve: Whole = (40 / 75) * 100 = 53.33. Since we can't have a fraction of a question, the student answered 53 questions correctly.

3. Finding the Percentage Increase or Decrease:

Problem: The price of a house increased from $200,000 to $250,000. What is the percentage increase?

Solution:

• Identify the "Original Value": The initial price of the house, $200,000.
• Identify the "Change": The difference between the new and old price, $50,000.
• Apply the formula: Percentage Increase = (Change / Original Value) * 100
• Solve: Percentage Increase = ($50,000 / $200,000) * 100 = 25%

4. Percentage Problems with Multiple Variables:

Problem: A store offers a 20% discount on all items. If you buy a shirt for $25 and a pair of pants for $40, what is the total discount and the final price?

Solution:

• Calculate the discount for each item:
  • Shirt discount: (20/100) * $25 = $5
  • Pants discount: (20/100) * $40 = $8
• Calculate the total discount: $5 + $8 = $13
• Calculate the total price before the discount: $25 + $40 = $65
• Calculate the final price: $65 - $13 = $52

Helpful Tips for Solving Percentage Word Problems:

• Read carefully: Understand the problem before attempting to solve it.
• Identify the key information: What are the "Part," "Whole," and "Percentage"?
• Use the correct formula: Apply the appropriate formula to find the unknown variable.
• Check your answer: Does your answer make sense in the context of the problem?

Conclusion:

Percentage word problems are a valuable skill to have. By understanding the fundamental formula and applying a logical approach, you can confidently solve a wide range of these problems encountered in everyday life. Remember to break down complex problems into smaller steps and always double-check your answers.