Percent Word Problems Worksheet With Answers - Easy Guide
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When it comes to understanding percentages, word problems can often seem daunting. However, with a little bit of practice and a clear strategy, you can tackle these problems with confidence. This article will provide you with an easy guide to solving percent word problems, complete with examples and a worksheet to test your knowledge. 📊
What is a Percent? 💡
Before diving into word problems, let’s establish what a percent is. A percent represents a number out of 100. The word itself comes from the Latin phrase "per centum," meaning "by the hundred." For instance, 25% means 25 out of 100.
Common Terms Used in Percent Problems 🔑
When working with percent problems, certain terms frequently appear. Here are a few key terms to remember:
- Increase: When a quantity goes up, which means you will be calculating the new total after adding a percentage.
- Decrease: When a quantity goes down, which involves subtracting the percentage from the original value.
- Of: This usually indicates multiplication in percent problems.
- Is: This often indicates equality in the context of the problem.
Step-by-Step Approach to Solve Percent Problems 🛠️
- Read the Problem Carefully: Understand what is being asked.
- Identify the Values: Determine what the total amount is, what percent you are working with, and if it involves an increase or decrease.
- Translate the Words into Numbers: Convert the words of the problem into a mathematical equation.
- Solve the Equation: Perform the calculations needed to find your answer.
- Check Your Work: Make sure your answer makes sense in the context of the problem.
Example Problems 📘
Let’s walk through a few example problems to illustrate the approach.
Example 1: Finding a Percentage
Problem: A student scored 80 out of 100 on a test. What percentage did the student score?
Solution:
- Total = 100
- Score = 80
To find the percentage:
[ \text{Percentage} = \left(\frac{\text{Score}}{\text{Total}}\right) \times 100 = \left(\frac{80}{100}\right) \times 100 = 80% ]
Example 2: Finding the Total with a Given Percentage
Problem: If 20% of a number is 50, what is the number?
Solution:
Let ( x ) be the unknown number.
[ 0.20 \times x = 50 ]
To find ( x ):
[ x = \frac{50}{0.20} = 250 ]
Example 3: Increase and Decrease
Problem: A jacket originally costs $60 but is on sale for 25% off. How much is the sale price?
Solution:
- Find the discount amount:
[ \text{Discount} = 0.25 \times 60 = 15 ]
- Subtract the discount from the original price:
[ \text{Sale Price} = 60 - 15 = 45 ]
The sale price of the jacket is $45.
Percent Word Problems Worksheet 📝
To practice your skills, here’s a worksheet with various percent word problems.
<table> <tr> <th>Problem</th> <th>Answer</th> </tr> <tr> <td>A shirt costs $40. If it is marked down by 10%, what is the sale price?</td> <td></td> </tr> <tr> <td>In a class of 30 students, 40% received an A. How many students got an A?</td> <td></td> </tr> <tr> <td>A car is priced at $25,000 with a 5% sales tax. What is the total price including tax?</td> <td></td> </tr> <tr> <td>After a 15% increase, a product costs $46. What was the original price?</td> <td></td> </tr> </table>
Important Note: Use the methods outlined in this article to solve each problem. Be sure to show your work for full understanding!
Answers to the Worksheet 🔍
-
Sale Price of the Shirt:
- Discount = $40 × 0.10 = $4
- Sale Price = $40 - $4 = $36
-
Number of Students who got an A:
- Students with A = 30 × 0.40 = 12
-
Total Price with Sales Tax:
- Tax Amount = $25,000 × 0.05 = $1,250
- Total Price = $25,000 + $1,250 = $26,250
-
Original Price before Increase:
- Let ( x ) be the original price, thus:
- ( x + 0.15x = 46 )
- ( 1.15x = 46 )
- ( x = \frac{46}{1.15} \approx 40 )
By practicing these types of problems, you’ll improve your skills in working with percentages. Remember, the key to mastering percent word problems is to stay calm, understand the problem, and methodically apply the steps outlined in this guide. Good luck, and happy calculating! 📈✨