Introduction to Percent Equations

Today, we’re going to learn about solving percent equations through word problems. This is an important skill that helps us understand how percentages work in real life. Let’s break it down step by step!

What is a Percent?

A percent means “out of 100.” For example, if you have 25%, it means 25 out of every 100.

How to Solve Percent Problems

When solving percent problems, we often use the formula:

\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100

To find the part or the whole, we can rearrange the formula.

  • Finding the Part:

\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}

  • Finding the Whole:

\text{Whole} = \frac{\text{Part}}{\text{Percent}} \times 100

Steps to Solve Word Problems

  1. Read the Problem Carefully: Identify what the question is asking.
  2. Highlight Important Information: Look for numbers and keywords like “percent,” “of,” and “total.”
  3. Choose the Right Formula: Decide if you need to find the part, the whole, or the percent.
  4. Do the Math: Substitute the numbers into the formula and solve.
  5. Check Your Work: Make sure your answer makes sense in the context of the problem.

Example Problems

Example 1:

A school has 200 students. If 25% of the students are girls, how many girls are there?

  1. Identify the Whole: 200 students (this is the whole).
  2. Identify the Percent: 25%.
  3. Use the Formula: \text{Part} = \frac{25}{100} \times 200 = 50
  4. Conclusion: There are 50 girls in the school.

Example 2:

If 30 students in a class scored 70% on their test, how many students took the test?

  1. Identify the Part: 30 students (this is the part).
  2. Identify the Percent: 70%.
  3. Use the Formula: \text{Whole} = \frac{30}{70} \times 100 \approx 42.86
    Since we can’t have a fraction of a student, we can round to 43.
  4. Conclusion: Approximately 43 students took the test.

Key Rules to Remember

  • Always convert the percent to a decimal when calculating.
  • When you see “of,” it usually means to multiply.
  • Make sure your final answer makes sense in the context of the problem.

Tips and Tricks

  • Use a calculator to help with larger numbers.
  • Write down your steps to avoid confusion.
  • Double-check your answers by plugging them back into the original question.

Questions

Easy Level Questions

  1. What is 10% of 50?
  2. If 25% of 80 is what number?
  3. How many is 20% of 200?
  4. A shirt costs £20. What is 15% off?
  5. There are 40 students in a class. If 50% are boys, how many boys are there?
  6. What is 5% of 60?
  7. If a book costs £40 and is 25% off, what is its new price?
  8. What is 30% of 90?
  9. A pizza is cut into 10 slices. If I eat 40%, how many slices did I eat?
  10. What is 80% of 25?

Medium Level Questions

  1. A car is priced at £12,000. If it is discounted by 20%, what is the new price?
  2. If 15% of a number is 30, what is the number?
  3. A school has 500 students. If 12% are in the football team, how many are in the team?
  4. If a jacket costs £50 and is on sale for 30% off, how much do you save?
  5. What is 75% of 160?
  6. A class has 24 students. If 1/3 are girls, how many girls are there?
  7. If 50% of 200 is what number?
  8. A ticket costs £25. If you get a 10% student discount, how much do you pay?
  9. What is 90% of 80?
  10. If a game is priced at £30 and is on sale for 20% off, what is the discount amount?

Hard Level Questions

  1. If a laptop originally costs £800 and is on sale for 25% off, what is the sale price?
  2. A recipe calls for 60 grams of sugar, which is 15% of the total weight of the ingredients. What is the total weight?
  3. If 8 out of 40 students passed a test, what percentage passed?
  4. A shop sells 200 items. If 30% are sold in a sale, how many are left?
  5. A dress costs £120. If it is marked down by 40%, what is the final price?
  6. If a student scores 85% in an exam with 60 questions, how many questions did they answer correctly?
  7. A restaurant bill is £50. If you tip 15%, how much do you tip?
  8. If 45 is 75% of a number, what is the number?
  9. A school has 300 students; 20% are new. How many new students are there?
  10. A car is worth £15,000. If it depreciates by 10% each year, what will it be worth after one year?

Answers

Easy Level Answers

  1. £5
  2. 20
  3. £40
  4. £17
  5. 20 boys
  6. £3
  7. £30
  8. £27
  9. 4 slices
  10. £20

Medium Level Answers

  1. £9,600
  2. 200
  3. 60 students
  4. £15
  5. £120
  6. 8 girls
  7. 100
  8. £22.50
  9. £72
  10. £6

Hard Level Answers

  1. £600
  2. 400 grams
  3. 20%
  4. 140 items
  5. £72
  6. 51 questions
  7. £7.50
  8. 60
  9. 60 new students
  10. £13,500

I hope this helps you understand how to solve percent equations through word problems! Remember to practice, and you’ll get better at it!