Solve equations: word problems
| What Are Word Problems? |
- Word problems describe a real-life situation using words.
- We use equations to represent these situations mathematically and then solve for unknowns.
| Steps to Solve Word Problems Using Equations |
- Read the problem carefully.
- Identify the unknown quantity and assign a variable (e.g., xxx).
- Translate the words into an equation using the variable.
- Simplify and solve the equation step-by-step.
- Check your solution by substituting the value back into the problem context.
- Write the answer clearly with units.
| Key Phrases and Their Mathematical Meanings |
| Word Phrase | Mathematical Operation |
|---|---|
| Sum of | Addition (+) |
| Difference between | Subtraction (–) |
| Product of | Multiplication (×) |
| Quotient of | Division (÷) |
| More than / Increased by | Addition (+) |
| Less than / Decreased by | Subtraction (–) |
| Twice / Double | Multiply by 2 |
| Three times / Triple | Multiply by 3 |
| Equal to / Is | Equals (=) |
| Examples |
Example 1:
The sum of a number and 7 is 15. Find the number.
- Let the number be x
- Equation: x+7=15
- Solve: x=15−7=8
- Answer: The number is 8.
Example 2:
Five times a number decreased by 3 is 12. Find the number.
- Let the number be x.
- Equation: 5x−3=12
- Solve: 5x=12+3=15
- x=155=3
- Answer: The number is 3.
Example 3:
A rectangle has length 3 meters more than twice its width. The perimeter is 36 meters. Find the length and width.
- Let width = w meters.
- Length = 2w+3 meters.
- Perimeter formula: 2(length+width)=36
- Equation: 2((2w+3)+w)=36
- Simplify: 2(3w+3)=36
- 6w=30→ w=5 meters
- Length: 2(5)+3=13 meters
- Answer: Width = 5 m, Length = 13 m.
| Tips for Success |
- Always define the variable clearly.
- Translate phrases carefully into mathematical expressions.
- Don’t forget units (meters, liters, rupees, etc.) in your final answer.
- Check your answer by plugging it back into the problem statement.
- Practice regularly to improve translation and solving skills.
| Practice Problems |
- The difference between a number and 8 is 14. Find the number.
- Twice a number increased by 5 is 21. Find the number.
- The sum of three consecutive numbers is 51. Find the numbers.
- A number divided by 4 and then increased by 7 gives 13. Find the number.
- The length of a rectangle is 4 meters more than its width. The perimeter is 28 meters. Find the dimensions.
Learn with an example
Alexandra can bake 9 biscuits with each scoop of flour. How many scoops of flour does Alexandra need in order to bake 36 biscuits?
———scoops
Write an equation that shows how the number of biscuits Alexandra can bake depends on the number of scoops of flour f. Then solve.
36=9 . f
4=f divide both sides by 9
To bake 36 biscuits, Alexandra needs 4 scoops of flour.
Camille can grow 5 flowers with every seed packet. How many seed packets does Camille need to have a total of 25 flowers in her garden?
—-seed packets.
Write an equation that shows how the total number of flowers depends on the number of seed packets used s. Then solve.
25 = 5 · s
5 = s Divide both sides by 5
To have a total of 25 flowers in her garden, Camille needs 5 seed packets.
Jonathan can grow 4 plants with every seed packet. How many seed packets does Jonathan need to have a total of 24 plants in his back garden?
—- seed packets.
Write an equation that shows how the total number of plants depends on the number of seed packets used s. Then solve.
24 = 4 · s
6 = s Divide both sides by 4
To have a total of 24 plants in his back garden,Jonathan needs 6 seed packets.
let’s practice!
