Year 7 Maths: Solve One-Step Equations- Word Problems

Introduction

Hello, Year 7! Today, we’re going to learn how to solve one-step equations through word problems. This is an important skill that helps us translate everyday situations into mathematical equations. Let’s break it down step by step!

What is a One-Step Equation?

A one-step equation is an equation that can be solved in just one step. This usually involves either adding, subtracting, multiplying, or dividing. For example, if we have:

We can solve it in one step by subtracting 5 from both sides.

How to Solve Word Problems

When we have a word problem, we need to follow these steps:

1. Read the Problem Carefully: Understand what is being asked.
2. Identify the Unknown: Decide what you need to find (this will often be represented by a letter, like (x)).
3. Translate to an Equation: Change the words into a mathematical equation.
4. Solve the Equation: Use the correct operation to isolate the unknown.
5. Check Your Answer: Make sure your answer makes sense in the context of the problem.

Examples

Example 1:

Problem: Sarah has some apples. She buys 8 more and now has 15 apples. How many apples did she start with?

Step 1: Identify the unknown. Let (x) be the number of apples Sarah started with.

Step 2: Translate the problem into an equation:

Step 3: Solve the equation by subtracting 8 from both sides:

Step 4: Check your answer. If Sarah started with 7 apples and bought 8 more, she now has 15 apples. This is correct!

Example 2:

Problem: Tom has some money. If he spends £4, he has £10 left. How much money did he have initially?

Step 1: Let (x) be the amount of money Tom had.

Step 2: Write the equation:

Step 3: Solve the equation by adding 4 to both sides:

Step 4: Check your answer. If Tom had £14 and spent £4, he would have £10 left. This is correct!

Key Rules

1. Use Inverse Operations: To isolate the variable, use the opposite operation. If it’s addition, use subtraction; if it’s multiplication, use division.
2. Keep the Equation Balanced: Whatever you do to one side of the equation, do to the other side too.
3. Write Clearly: Always show your working out. This helps you keep track of your thought process.

Tips and Tricks

• Keywords: Look for keywords in the problem:
  • “More than” usually means addition.
  • “Left” or “Remaining” usually means subtraction.
  • “Each” or “Total” can suggest multiplication.
• Draw a Picture: Sometimes drawing a diagram can help you understand the problem better.
• Practice: The more you practice, the easier it will become!

Questions

Easy Level Questions

1. If (x + 3 = 10), what is (x)?
2. David has (x) toys. He buys 2 more and now has 5. Write the equation and solve for (x).
3. If (x – 6 = 4), what is (x)?
4. A number decreased by 1 equals 9. What is the number?
5. If (x + 4 = 12), find (x).
6. A bike costs (x) pounds. After spending £5, the cost is £45. Write the equation and solve for (x).
7. If (x – 2 = 3), what is (x)?
8. Sarah has (x) pencils. She buys 10 and now has 20. Write the equation and solve for (x).
9. If (x + 5 = 15), find (x).
10. A number added to 7 equals 12. What is the number?

Medium Level Questions

11. If (x + 7 = 20), what is (x)?
12. Anna had (x) pounds. After spending £3, she has £12 left. Write the equation and solve for (x).
13. If (x – 5 = 15), what is (x)?
14. A number is multiplied by 3 and equals 15. What is the number?
15. If (x + 10 = 30), find (x).
16. Tom has (x) candies. After giving away 4, he has 12 left. Write the equation and solve for (x).
17. If (x – 3 = 11), what is (x)?
18. A book costs (x) pounds. After a discount of £5, the price is £10. Write the equation and solve for (x).
19. If (x + 2 = 9), find (x).
20. A number decreased by 4 equals 16. What is the number?

Hard Level Questions

21. If (x + 15 = 35), what is (x)?
22. Lisa had £x. After buying a shirt for £8, she has £12 left. Write the equation and solve for (x).
23. If (x – 7 = 21), what is (x)?
24. A number multiplied by 5 is 25. What is the number?
25. If (x + 20 = 50), find (x).
26. Mark has (x) stickers. After giving away 6, he has 14 left. Write the equation and solve for (x).
27. If (x – 8 = 12), what is (x)?
28. A toy costs £x. After a sale of £10, the price is £20. Write the equation and solve for (x).
29. If (x + 4 = 18), find (x).
30. A number decreased by 10 equals 30. What is the number?

Answers

Easy Level Answers

1. (x = 7)
2. (x = 3)
3. (x = 10)
4. 10
5. (x = 8)
6. (x = 50)
7. (x = 5)
8. (x = 10)
9. (x = 10)
10. 5

Medium Level Answers

11. (x = 13)
12. (x = 15)
13. (x = 20)
14. 5
15. (x = 20)
16. (x = 16)
17. (x = 14)
18. (x = 15)
19. (x = 7)
20. 20

Hard Level Answers

21. (x = 20)
22. (x = 20)
23. (x = 28)
24. 5
25. (x = 30)
26. (x = 20)
27. (x = 20)
28. (x = 30)
29. (x = 14)
30. 40

Conclusion

Now you know how to solve one-step equations using word problems! Remember to practice regularly, and don’t hesitate to ask if you’re unsure about something. Happy solving!