Translating Words to Equations
Learn to convert word problems into algebraic equations you can solve.
Definition
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Worked Examples
"A number increased by 7 equals 15." Write as an equation.
Identify the unknown
"A number" is unknown → Let = the number
Find the operation word
"increased by" means addition →
Find the result
"equals 15" means →
Answer: (solving: )
Common Mistakes
Reversing subtraction: Writing "5 less than " as instead of
Why it's wrong: "Less than" means you subtract from the number. "5 less than " = " minus 5"
Correct: "5 less than " translates to , not
Forgetting parentheses: Writing "3 times the sum of and 2" as
Why it's wrong: "The sum of and 2" is a group that gets multiplied. Without parentheses, only gets multiplied.
Correct: "3 times the sum of and 2" is , not
Confusing "more than" with "is more than": " is 5 more than " vs. " is more than 5"
Why it's wrong: "5 more than " means . "Is more than" is a comparison (inequality).
Correct: " is 5 more than " means
Interactive Visual
Balance Scale
Solution: x = 4
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsWhich equation represents "a number increased by 5 equals 12"?
Why It Matters
- Shopping: "The total cost is 15 dollars more than twice the original price"
- Cooking: "The recipe serves 4 people. How much for 10 people?"
- Sports: "She scored 5 fewer points than triple her last game"
- Work: "You earn 12 dollars per hour plus a 25 dollar bonus"
Real World Applications
Shopping and Discounts
Stores describe prices in words that you can translate to find deals.
Example:
"The sale price is 20 dollars less than the original price" becomes , where is sale price and is original price.
A shirt costs 15 dollars more than twice the cost of a hat. The shirt costs 45 dollars.
How much does the hat cost?
Step 1: Write the mathematical expression
Let = hat cost. Write the equation:
Salary and Earnings
Job pay is often described in words that become equations.
Example:
"You earn 15 dollars per hour plus a 50 dollar bonus" becomes , where is total earnings and is hours worked.
You earn 12 dollars per hour. After working some hours and adding a 30 dollar tip, you have 90 dollars total.
How many hours did you work?
Step 1: Write the mathematical expression
Let = hours worked. Write the equation:
Sports Statistics
Athletes' stats are compared using phrases that translate to equations.
Example:
"She scored 8 more points than her previous game" becomes , where is this game's score and is the previous score.
In the final, Tom scored triple his semifinal points minus 5. He scored 25 points in the final.
How many points did Tom score in the semifinal?
Step 1: Write the mathematical expression
Let = semifinal points. Write the equation:
Key Takeaways
- 1Identify unknowns and assign variables (usually )
- 2Learn key phrases: 'sum' = add, 'difference' = subtract, 'product' = multiply, 'quotient' = divide
- 3Watch for order: '5 less than ' is , not
- 4Use parentheses for grouped operations: '3 times the sum' =
- 5Translate step by step, then solve the equation
Frequently Asked Questions
Glossary
- Variable
- A letter that represents an unknown value (e.g., , , )
- Expression
- A mathematical phrase with numbers, variables, and operations but no equals sign (e.g., )
- Equation
- A mathematical statement with an equals sign showing two expressions are equal (e.g., )
- Coefficient
- The number multiplied by a variable (in , the coefficient is 3)
- Sum
- The result of adding numbers ()
- Difference
- The result of subtracting numbers ()
- Product
- The result of multiplying numbers ()
- Quotient
- The result of dividing numbers ()