Introduction

Hello, Year 7! Today, we are going to learn how to solve one-step equations using word problems. This is a great way to use maths in real-life situations. Let’s break it down step by step.

What is a One-Step Equation?

A one-step equation is a mathematical statement that shows two things are equal, and we can solve it in one step. For example, if we have an equation like x + 5 = 12

, we need to find out what x
is. In this case, we would subtract 5 from both sides to find that x = 7
.

Solving Word Problems

When we have a word problem, it’s all about understanding what the problem is asking and turning it into an equation. Let’s look at a few steps to help us solve these problems:

  1. Read the Problem Carefully: Understand what is happening.
  2. Identify Key Information: Look for numbers and keywords like “more than”, “less than”, “total”, or “together”.
  3. Write an Equation: Turn the words into a mathematical equation.
  4. Solve the Equation: Use the correct operation to find the answer.
  5. Check Your Work: Make sure your answer makes sense in the context of the problem.

Example 1

Problem: Emma has some marbles. If she gets 8 more marbles, she will have 20 marbles. How many marbles does Emma have now?

  1. Identify the unknown: Let x
    be the number of marbles Emma has.
  2. Write the equation: x + 8 = 20
    .
  3. Solve the equation: Subtract 8 from both sides: x = 20 – 8
    , so x = 12
    .
  4. Check: If Emma has 12 marbles and gets 8 more, she indeed has 20 marbles.

Example 2

Problem: A book costs £15 less than a game. If the game costs £30, how much does the book cost?

  1. Identify the unknown: Let x
    be the cost of the book.
  2. Write the equation: x + 15 = 30
    .
  3. Solve the equation: Subtract 15 from both sides: x = 30 – 15
    , so x = 15
    .
  4. Check: If the book costs £15, then £15 + £15 is indeed £30.

Key Rules to Remember

  • Always perform the same operation on both sides of the equation.
  • Keep the equation balanced, like a seesaw.
  • Check your work to make sure your answer makes sense.

Tips and Tricks

  • Use drawings or diagrams to visualise the problem.
  • Write down what you know and what you need to find out.
  • Practice with different word problems to get better!

Questions

Easy Level Questions

  1. A number is increased by 7 and equals 14. What is the number?
  2. Sam has some stickers. If he gets 5 more, he will have 12. How many does he have now?
  3. A basket has 10 apples. If you add x
    more apples and have 15 apples in total, what is x
    ?
  4. A toy costs £8 less than a game. If the game costs £20, how much is the toy?
  5. If you subtract 4 from a number, you get 10. What is the number?
  6. A number is decreased by 3 and equals 9. What is the number?
  7. There are x
    birds in a tree. If 5 more join them, there are 12. How many birds were there originally?
  8. A bag has x
    candies. If you eat 2 and have 5 left, how many candies were there to start?
  9. A number is 6 more than 4. What is the number?
  10. If you add 2 to a number, you get 11. What is the number?
  11. You have x
    coins. If you find 3 more, you have 8 coins in total. How many do you have?
  12. A pen costs 3 pounds less than a pencil. If the pencil costs 7 pounds, how much is the pen?
  13. If a number is 5 less than 12, what is the number?
  14. A number added to 10 gives you 20. What is the number?
  15. If you take away 7 from a number, you are left with 2. What is the number?
  16. A book has x
    pages. If you read 5 pages, you have 20 pages left. How many pages does the book have?
  17. A car costs £15,000. If you save £2,000, how much more do you need to save?
  18. You have x
    sweets. If you give away 4 and have 6 left, how many did you start with?
  19. A garden has 10 flowers. If you plant x
    more and have 15 in total, what is x
    ?
  20. If you add 1 to a number, you get 5. What is the number?

Medium Level Questions

  1. A number multiplied by 3 equals 15. What is the number?
  2. If you subtract 6 from twice a number, you get 12. What is the number?
  3. A number is divided by 4 and equals 5. What is the number?
  4. Jamie has x
    pencils. If he buys 3 more, he has 10 pencils in total. How many did he start with?
  5. A train travels x miles per hour. If it travels for 3 hours and covers 180 miles, what is x?
  6. If you subtract 2 from a number and multiply by 3, you get 12. What is the number?
  7. A jacket costs £50. If it is on sale for £x, and the sale price is £30, what is x?
  8. A number is 4 times another number. If the second number is 3, what is the first number?
  9. If you add 10 to a number and then divide by 2, you get 15. What is the number?
  10. A movie ticket costs £x. If you buy 4 tickets for £32, what is x?
  11. A box has x
    chocolates. If you eat 5 and have 25 left, how many were there?
  12. A number divided by 2 gives you 10. What is the number?
  13. A number is increased by 9 and equals 28. What is the number?
  14. If you subtract 3 from a number, you get 7. What is the number?
  15. A box of toys costs £x. If you buy 5 boxes for £75, what is x?
  16. If you add 4 to a number and multiply by 2, you get 20. What is the number?
  17. A car travels x
    miles in 1 hour. If it travels 120 miles in 2 hours, what is x?
  18. A number is decreased by 4 and equals 11. What is the number?
  19. If you multiply a number by 5 and subtract 5, you get 10. What is the number?
  20. A number is 3 times another number. If the second number is 2, what is the first number?

Hard Level Questions

  1. A number multiplied by itself equals 100. What is the number?
  2. If three times a number plus 4 equals 22, what is the number?
  3. A number divided by 5, minus 3, equals 2. What is the number?
  4. If the sum of a number and 7 is equal to twice the number, what is the number?
  5. A number is 5 more than twice another number. If the second number is 4, what is the first number?
  6. A number minus 6 equals 4 times that number. What is the number?
  7. If you subtract 3 from a number and multiply by 6, you get 24. What is the number?
  8. A number is decreased by 5 and equals 3 times another number. If the second number is 2, what is the first number?
  9. If the product of a number and 7 equals 42, what is the number?
  10. A number is 8 less than 3 times another number. If the second number is 5, what is the first number?
  11. If you add 2 to a number and square the result, you get 36. What is the number?
  12. The difference between a number and 10 equals twice that number. What is the number?
  13. A number divided by 3 equals 4 less than the number. What is the number?
  14. If you take a number, double it, and then subtract 6, you get 18. What is the number?
  15. A number is increased by 12 and equals 5 times that number. What is the number?
  16. If you multiply a number by 4 and then add 8, you get 32. What is the number?
  17. A number is 9 less than 3 times another number. If the second number is 6, what is the first number?
  18. If the sum of three times a number and 5 equals 20, what is the number?
  19. A number divided by 4 plus 2 equals 10. What is the number?
  20. If you subtract a number from 8 and the result is 2, what is the number?

Answers and Explanations

Easy Level Answers

  1. x + 7 = 14
    ; so x = 14 – 7 = 7
    .
  2. x + 5 = 12
    ; so x = 12 – 5 = 7
    .
  3. 10 + x = 15
    ; so x = 15 – 10 = 5
    .
  4. x + 8 = 20
    ; so x = 20 – 8 = 12
    .
  5. x – 4 = 10
    ; so x = 10 + 4 = 14
    .
  6. x – 3 = 9
    ; so x = 9 + 3 = 12
    .
  7. x + 5 = 12
    ; so x = 12 – 5 = 7
    .
  8. x – 2 = 5
    ; so x = 5 + 2 = 7
    .
  9. x + 6 = 4
    ; so x = 4 – 6 = -2
    .
  10. x + 2 = 11
    ; so x = 11 – 2 = 9
    .
  11. x + 3 = 8
    ; so x = 8 – 3 = 5
    .
  12. x + 3 = 7
    ; so x = 7 – 3 = 4
    .
  13. x – 5 = 12
    ; so x = 12 + 5 = 17
    .
  14. x + 10 = 20
    ; so x = 20 – 10 = 10
    .
  15. x – 7 = 2
    ; so x = 2 + 7 = 9
    .
  16. x – 5 = 20
    ; so x = 20 + 5 = 25
    .
  17. x – 2 = 12
    ; so x = 12 + 2 = 14
    .
  18. x + 10 = 15
    ; so x = 15 – 10 = 5
    .
  19. x + 10 = 15
    ; so x = 15 – 10 = 5
    .
  20. x + 1 = 5
    ; so x = 5 – 1 = 4
    .

Medium Level Answers

  1. 3x = 15
    ; so x = 15/3 = 5
    .
  2. 2x – 6 = 12
    ; so 2x = 12 + 6 = 18
    ; thus, x = 18/2 = 9
    .
  3. x/4 = 5
    ; so x = 5 \times 4 = 20
    .
  4. x + 7 = 2x
    ; so x = 7
    .
  5. x = 2 \cdot 4 + 5 = 13
    .
  6. x – 2 \cdot 3 = 12
    ; so x = 12 + 6 = 18
    .
  7. x = 50 – 30 = 20
    .
  8. x = 4 \cdot 3 = 12
    .
  9. x + 10 = 30
    ; so x = 30 – 10 = 20
    .
  10. x = 32/4 = 8
    .
  11. x – 5 = 25
    ; so x = 25 + 5 = 30
    .
  12. x/2 = 10
    ; so x = 10 \times 2 = 20
    .
  13. x + 9 = 28
    ; so x = 28 – 9 = 19
    .
  14. x – 3 = 7
    ; so x = 7 + 3 = 10
    .
  15. x = 75/5 = 15
    .
  16. 2x + 4 = 20
    ; so 2x = 20 – 4 = 16
    ; thus, x = 8
    .
  17. x = 120/2 = 60
    .
  18. x – 5 = 11
    ; so x = 11 + 5 = 16
    .
  19. x/4 + 2 = 10
    ; so x/4 = 10 – 2 = 8
    ; thus, x = 32
    .
  20. 8 – x = 2
    ; so x = 8 – 2 = 6
    .

Hard Level Answers

  1. x^2 = 100
    ; so x = 10
    (or -10
    ).
  2. 3x + 4 = 22
    ; so 3x = 22 – 4 = 18
    ; thus, x = 6
    .
  3. x/5 – 3 = 2
    ; so x/5 = 5
    ; thus, x = 25
    .
  4. x + 7 = 2x
    ; so x = 7
    .
  5. x = 2 \cdot 4 + 5 = 13
    .
  6. x – 6 = 4x
    ; so 3x = 6
    ; thus, x = 2
    .
  7. (x – 3) \cdot 6 = 24
    ; so x – 3 = 4
    ; thus, x = 7
    .
  8. x – 5 = 2 \cdot 2
    ; so x = 4 + 5 = 9
    .
  9. x \cdot 7 = 42
    ; so x = 42/7 = 6
    .
  10. x = 3 \cdot 5 – 8 = 7
    .
  11. (x + 2)^2 = 36
    ; so x + 2 = 6 \text{ or } x + 2 = -6
    ; thus, x = 4 \text{ or } -8
    .
  12. 8 – x = 2x
    ; so 3x = 8
    ; thus, x = 8/3
    .
  13. x/3 = x – 4
    ; so 4 = 3x
    ; thus, x = 12
    .
  14. 2x – 6 = 18
    ; so 2x = 24
    ; thus, x = 12
    .
  15. x + 12 = 5x
    ; so 4x = 12
    ; thus, x = 3
    .
  16. 4x + 8 = 32
    ; so 4x = 24
    ; thus, x = 6
    .
  17. 3x – 9 = 6
    ; so 3x = 15
    ; thus, x = 5
    .
  18. 3x + 5 = 20
    ; so 3x = 15
    ; thus, x = 5
    .
  19. x/4 + 2 = 10
    ; so x/4 = 8
    ; thus, x = 32
    .
  20. 8 – x = 2
    ; so x = 8 – 2 = 6
    .

Conclusion

Now you know how to solve one-step equations using word problems! Remember to read carefully, write your equations, and check your answers. Keep practising, and you’ll get even better at it!