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

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!