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
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:
- Read the Problem Carefully: Understand what is happening.
- Identify Key Information: Look for numbers and keywords like “more than”, “less than”, “total”, or “together”.
- Write an Equation: Turn the words into a mathematical equation.
- Solve the Equation: Use the correct operation to find the answer.
- 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?
- Identify the unknown: Let xbe the number of marbles Emma has.
- Write the equation: x + 8 = 20.
- Solve the equation: Subtract 8 from both sides: x = 20 – 8, so x = 12.
- 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?
- Identify the unknown: Let xbe the cost of the book.
- Write the equation: x + 15 = 30.
- Solve the equation: Subtract 15 from both sides: x = 30 – 15, so x = 15.
- 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
- A number is increased by 7 and equals 14. What is the number?
- Sam has some stickers. If he gets 5 more, he will have 12. How many does he have now?
- A basket has 10 apples. If you add xmore apples and have 15 apples in total, what is x?
- A toy costs £8 less than a game. If the game costs £20, how much is the toy?
- If you subtract 4 from a number, you get 10. What is the number?
- A number is decreased by 3 and equals 9. What is the number?
- There are xbirds in a tree. If 5 more join them, there are 12. How many birds were there originally?
- A bag has xcandies. If you eat 2 and have 5 left, how many candies were there to start?
- A number is 6 more than 4. What is the number?
- If you add 2 to a number, you get 11. What is the number?
- You have xcoins. If you find 3 more, you have 8 coins in total. How many do you have?
- A pen costs 3 pounds less than a pencil. If the pencil costs 7 pounds, how much is the pen?
- If a number is 5 less than 12, what is the number?
- A number added to 10 gives you 20. What is the number?
- If you take away 7 from a number, you are left with 2. What is the number?
- A book has xpages. If you read 5 pages, you have 20 pages left. How many pages does the book have?
- A car costs £15,000. If you save £2,000, how much more do you need to save?
- You have xsweets. If you give away 4 and have 6 left, how many did you start with?
- A garden has 10 flowers. If you plant xmore and have 15 in total, what is x?
- If you add 1 to a number, you get 5. What is the number?
Medium Level Questions
- A number multiplied by 3 equals 15. What is the number?
- If you subtract 6 from twice a number, you get 12. What is the number?
- A number is divided by 4 and equals 5. What is the number?
- Jamie has xpencils. If he buys 3 more, he has 10 pencils in total. How many did he start with?
- A train travels x miles per hour. If it travels for 3 hours and covers 180 miles, what is x?
- If you subtract 2 from a number and multiply by 3, you get 12. What is the number?
- A jacket costs £50. If it is on sale for £x, and the sale price is £30, what is x?
- A number is 4 times another number. If the second number is 3, what is the first number?
- If you add 10 to a number and then divide by 2, you get 15. What is the number?
- A movie ticket costs £x. If you buy 4 tickets for £32, what is x?
- A box has xchocolates. If you eat 5 and have 25 left, how many were there?
- A number divided by 2 gives you 10. What is the number?
- A number is increased by 9 and equals 28. What is the number?
- If you subtract 3 from a number, you get 7. What is the number?
- A box of toys costs £x. If you buy 5 boxes for £75, what is x?
- If you add 4 to a number and multiply by 2, you get 20. What is the number?
- A car travels xmiles in 1 hour. If it travels 120 miles in 2 hours, what is x?
- A number is decreased by 4 and equals 11. What is the number?
- If you multiply a number by 5 and subtract 5, you get 10. What is the number?
- A number is 3 times another number. If the second number is 2, what is the first number?
Hard Level Questions
- A number multiplied by itself equals 100. What is the number?
- If three times a number plus 4 equals 22, what is the number?
- A number divided by 5, minus 3, equals 2. What is the number?
- If the sum of a number and 7 is equal to twice the number, what is the number?
- A number is 5 more than twice another number. If the second number is 4, what is the first number?
- A number minus 6 equals 4 times that number. What is the number?
- If you subtract 3 from a number and multiply by 6, you get 24. What is the number?
- A number is decreased by 5 and equals 3 times another number. If the second number is 2, what is the first number?
- If the product of a number and 7 equals 42, what is the number?
- A number is 8 less than 3 times another number. If the second number is 5, what is the first number?
- If you add 2 to a number and square the result, you get 36. What is the number?
- The difference between a number and 10 equals twice that number. What is the number?
- A number divided by 3 equals 4 less than the number. What is the number?
- If you take a number, double it, and then subtract 6, you get 18. What is the number?
- A number is increased by 12 and equals 5 times that number. What is the number?
- If you multiply a number by 4 and then add 8, you get 32. What is the number?
- A number is 9 less than 3 times another number. If the second number is 6, what is the first number?
- If the sum of three times a number and 5 equals 20, what is the number?
- A number divided by 4 plus 2 equals 10. What is the number?
- If you subtract a number from 8 and the result is 2, what is the number?
Answers and Explanations
Easy Level Answers
- x + 7 = 14; so x = 14 – 7 = 7.
- x + 5 = 12; so x = 12 – 5 = 7.
- 10 + x = 15; so x = 15 – 10 = 5.
- x + 8 = 20; so x = 20 – 8 = 12.
- x – 4 = 10; so x = 10 + 4 = 14.
- x – 3 = 9; so x = 9 + 3 = 12.
- x + 5 = 12; so x = 12 – 5 = 7.
- x – 2 = 5; so x = 5 + 2 = 7.
- x + 6 = 4; so x = 4 – 6 = -2.
- x + 2 = 11; so x = 11 – 2 = 9.
- x + 3 = 8; so x = 8 – 3 = 5.
- x + 3 = 7; so x = 7 – 3 = 4.
- x – 5 = 12; so x = 12 + 5 = 17.
- x + 10 = 20; so x = 20 – 10 = 10.
- x – 7 = 2; so x = 2 + 7 = 9.
- x – 5 = 20; so x = 20 + 5 = 25.
- x – 2 = 12; so x = 12 + 2 = 14.
- x + 10 = 15; so x = 15 – 10 = 5.
- x + 10 = 15; so x = 15 – 10 = 5.
- x + 1 = 5; so x = 5 – 1 = 4.
Medium Level Answers
- 3x = 15; so x = 15/3 = 5.
- 2x – 6 = 12; so 2x = 12 + 6 = 18; thus, x = 18/2 = 9.
- x/4 = 5; so x = 5 \times 4 = 20.
- x + 7 = 2x; so x = 7.
- x = 2 \cdot 4 + 5 = 13.
- x – 2 \cdot 3 = 12; so x = 12 + 6 = 18.
- x = 50 – 30 = 20.
- x = 4 \cdot 3 = 12.
- x + 10 = 30; so x = 30 – 10 = 20.
- x = 32/4 = 8.
- x – 5 = 25; so x = 25 + 5 = 30.
- x/2 = 10; so x = 10 \times 2 = 20.
- x + 9 = 28; so x = 28 – 9 = 19.
- x – 3 = 7; so x = 7 + 3 = 10.
- x = 75/5 = 15.
- 2x + 4 = 20; so 2x = 20 – 4 = 16; thus, x = 8.
- x = 120/2 = 60.
- x – 5 = 11; so x = 11 + 5 = 16.
- x/4 + 2 = 10; so x/4 = 10 – 2 = 8; thus, x = 32.
- 8 – x = 2; so x = 8 – 2 = 6.
Hard Level Answers
- x^2 = 100; so x = 10(or -10).
- 3x + 4 = 22; so 3x = 22 – 4 = 18; thus, x = 6.
- x/5 – 3 = 2; so x/5 = 5; thus, x = 25.
- x + 7 = 2x; so x = 7.
- x = 2 \cdot 4 + 5 = 13.
- x – 6 = 4x; so 3x = 6; thus, x = 2.
- (x – 3) \cdot 6 = 24; so x – 3 = 4; thus, x = 7.
- x – 5 = 2 \cdot 2; so x = 4 + 5 = 9.
- x \cdot 7 = 42; so x = 42/7 = 6.
- x = 3 \cdot 5 – 8 = 7.
- (x + 2)^2 = 36; so x + 2 = 6 \text{ or } x + 2 = -6; thus, x = 4 \text{ or } -8.
- 8 – x = 2x; so 3x = 8; thus, x = 8/3.
- x/3 = x – 4; so 4 = 3x; thus, x = 12.
- 2x – 6 = 18; so 2x = 24; thus, x = 12.
- x + 12 = 5x; so 4x = 12; thus, x = 3.
- 4x + 8 = 32; so 4x = 24; thus, x = 6.
- 3x – 9 = 6; so 3x = 15; thus, x = 5.
- 3x + 5 = 20; so 3x = 15; thus, x = 5.
- x/4 + 2 = 10; so x/4 = 8; thus, x = 32.
- 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!