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Questions and Answers
What is the relationship between a percentage and a fraction?
How would you calculate the percentage change between two values?
If 25% of a number is 30, what is that number?
What does it mean to find a percentage of a quantity?
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If an item's price increases by 20% from $50, what is the new price?
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What is the first step advised for solving word problems with percentages?
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In a group of 120 people, if 40% are women, how many women are in the group?
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If a laptop is initially priced at $800 and after a 15% discount its price becomes $680, what was the discounted amount?
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What is the final step recommended after solving a word problem with percentages?
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If a recipe calls for 2 cups of sugar, but you decide to reduce it by 20%, how many cups of sugar will you use?
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Study Notes
Solving Word Problems with Percentages
Percentages, often symbolized by the percent sign (%), are a fundamental part of mathematics and everyday life. In this article, we'll delve into word problems involving percentages, focusing on techniques and strategies for solving these types of problems effectively.
The Percentage Concept
A percentage is simply a fraction of 100, such as 75% (or 0.75) or 2% (or 0.02). When we use percentages in word problems, we're often asked to find a relationship between two quantities. For instance, we might be told that 60% of a group of students are female, and we need to determine how many female students there are in a total of 100 students.
Percentage Change
Percentage change problems ask us to find the difference between two quantities and express it as a percentage. For example, if the price of a book increases from $20 to $25, we might want to know what percentage the price increased. To solve this, calculate the difference between the two prices ($5) and divide by the original price ($20), then multiply by 100 to get the percentage.
[ \text{Percentage change} = \frac{\text{Difference}}{\text{Original}} \times 100 ]
Percentage of a Quantity
Sometimes, we're asked to find a percentage of a given quantity. For instance, if there are 100 apples and 20% of them are bruised, then there are 20/100 * 100 = 20 bruised apples.
Word Problems
While the percentage concepts themselves are relatively straightforward, word problems can be challenging due to the need to read and understand the given information. Here are some strategies for solving word problems with percentages:
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Understand the context: Make sure you have a clear understanding of the information provided, including the quantities and relationships between them.
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Identify the unknown quantity: Determine which quantity you are trying to find.
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Set up the problem: Decide which percentage concept is most appropriate for solving the problem. For example, if you're trying to find how much a certain item costs after a discount, use the percentage change concept.
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Perform the calculation: Use the appropriate percentage concept to find the unknown quantity.
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Check your answer: Confirm that your answer makes sense in the context of the problem.
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Refine your understanding: If the answer doesn't match your expectations, review your problem-solving steps and ensure you've used the correct percentage concept and performed the calculations correctly.
Example Problems
- If a group of 80 people includes 50% people who are left-handed, how many left-handed people are there in the group?
Answer: 50/100 * 80 = 40 left-handed people.
- A store sells 1000 shirts for $20 each. If the store offers a 30% discount, what is the new price of a shirt?
Answer: First, find the discounted price by subtracting 0.30 * 20 from 20: $20 - 0.30 * $20 = $14. Then, find the new price by dividing the discounted price by 0.70 (1 - 0.30): $14 / 0.70 = $20. However, since the original price was $20, there's no change, and the new price remains $20.
- A company makes 5000 products, but 30% of them are defective. How many defective products are there in the company's production?
Answer: 30/100 * 5000 = 1500 defective products.
- A town has a population of 10,000 people. If 75% of the people are registered to vote, how many registered voters are there in the town?
Answer: 75/100 * 10000 = 7500 registered voters.
- If the weight of a bag of potatoes decreases by 10% due to moisture, and the initial weight is 50 pounds, what is the weight of the bag after the decrease?
Answer: First, find the amount of weight lost by multiplying the initial weight by 0.10: 50 * 0.10 = 5. Then, find the new weight by subtracting the amount lost from the initial weight: 50 - 5 = 45 pounds.
These strategies and examples should help you solve word problems involving percentages more effectively. Remember that practice is key to mastering this topic, so don't be afraid to test your skills with new problems. Happy learning!
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Description
Delve into techniques for solving word problems involving percentages effectively. Understand concepts like percentage change and finding a percentage of a quantity through examples and strategies. Practice solving problems to enhance your skills in this area.
