Equation Word Problems
Learn to translate real-world situations into algebraic equations and solve them step by step.
Definition
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Worked Examples
Maria is 3 years older than twice her brother's age. If Maria is 17 years old, how old is her brother?
Define the variable
Let = brother's age → = unknown
Translate to equation
"3 years older than twice" means "Maria is 17" means equals 17 →
Subtract 3 from both sides
→
Divide both sides by 2
→
Check the answer
Twice 7 is 14, plus 3 is 17 ✓ → Brother is 7 years old
Answer: Maria's brother is years old.
Common Mistakes
Defining the wrong quantity as the variable
Why it's wrong: Choosing the larger or more complex quantity as makes the equation harder to solve.
Correct: Define as the simpler or smaller unknown. Express other quantities in terms of .
Forgetting to check if the answer makes sense
Why it's wrong: Mathematical solutions can be correct but not meaningful (e.g., negative ages).
Correct: Always verify: Does the answer fit the context? Is it positive when it should be? Does it satisfy the original problem?
Translating "less than" incorrectly
Why it's wrong: "5 less than x" is , NOT . Order matters with subtraction!
Correct: "A less than B" always means . The number that comes after "than" goes first.
Interactive Visual
Balance Scale
Solution: x = 4
Equation Solver
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Interactive Sandbox
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Practice Problems
18 problemsWhich equation represents: "A number increased by 7 equals 15"?
Why It Matters
- Shopping: Calculate sale prices, tax, or compare deals
- Cooking: Adjust recipe quantities for different serving sizes
- Sports: Calculate statistics, averages, and game scenarios
- Travel: Determine time, distance, or fuel needed
- Money: Budget expenses, calculate savings goals
Real World Applications
Event Planning
Event planners use equations to budget for venues, catering, and guest counts.
Example:
A venue charges 200 euros base fee plus 35 euros per guest. With a budget of 900 euros, how many guests can you invite?
A birthday party venue charges a 150 euro rental fee plus 12 euros per child. The total budget is 270 euros.
How many children can attend?
Step 1: Write the mathematical expression
Write the equation:
Sports Statistics
Athletes and coaches use equations to track performance and set goals.
Example:
A basketball player has scored 156 points in 12 games. How many points per game must she average in the next 8 games to reach 300 total points?
A runner has completed 42 km over 6 days. She wants to run a total of 70 km in 10 days.
How many km per day must she average for the remaining days?
Step 1: Write the mathematical expression
Points needed = Total goal - Points so far
Key Takeaways
- 1Read the problem carefully and identify what you need to find
- 2Define a variable (usually ) for the unknown quantity
- 3Translate key phrases into mathematical operations
- 4Write and solve the equation step by step
- 5Always check that your answer makes sense in the original context
Frequently Asked Questions
Glossary
- Variable
- A letter (like , , or ) that represents an unknown value
- Coefficient
- The number multiplied by a variable (in , the coefficient is 3)
- Constant
- A fixed number that doesn't change (like the base fee in a pricing problem)
- Translate
- Convert words into mathematical symbols and expressions
Formula Card
Key Translation Phrases
Common English phrases and their mathematical operators
Problem-Solving Framework
Five steps to solve any word problem