Equation Word Problems

Learn to translate real-world situations into algebraic equations and solve them step by step.

Intermediate25 minLesson
Printable worksheet

Definition

An equation word problem presents a real-world situation that can be solved by writing and solving an algebraic equation.
The key steps are:
  1. 1.Read the problem carefully and identify what you need to find
  2. 2.Define a variable for the unknown quantity
  3. 3.Translate the words into an equation
  4. 4.Solve the equation
  5. 5.Check your answer makes sense in context
Words→Equation→Solution\text{Words} \rightarrow \text{Equation} \rightarrow \text{Solution}

Try it now

Which equation represents: "A number increased by 7 equals 15"?

Worked Examples

Maria is 3 years older than twice her brother's age. If Maria is 17 years old, how old is her brother?
1

Define the variable

Let xx = brother's age → xx = unknown
2

Translate to equation

"3 years older than twice" means 2x+32x + 3 "Maria is 17" means equals 17 → 2x+3=172x + 3 = 17
3

Subtract 3 from both sides

2x+3−3=17−32x + 3 - 3 = 17 - 3 → 2x=142x = 14
4

Divide both sides by 2

2x2=142\frac{2x}{2} = \frac{14}{2} → x=7x = 7
5

Check the answer

Twice 7 is 14, plus 3 is 17 ✓ → Brother is 7 years old

Common Mistakes

Defining the wrong quantity as the variable

Why it's wrong: Choosing the larger or more complex quantity as xx makes the equation harder to solve.

Correct: Define xx as the simpler or smaller unknown. Express other quantities in terms of xx.

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 x−5x - 5, NOT 5−x5 - x. Order matters with subtraction!

Correct: "A less than B" always means B−AB - A. The number that comes after "than" goes first.

Interactive Visual

Balance Scale

2x + 3=17
2x
3
17
Apply to both sides:

Solution: x = 7

Equation Solver

Solve for xx:

2x+3=172x + 3 = 17
1
2x+3=172x + 3 = 17
Subtract 33 from both sidesRemove the constant term

Tips:

  • • Whatever you do to one side, do to the other
  • • Undo operations in reverse order (PEMDAS backwards)
  • • Check your answer by substituting back

Follow along as we solve the equation step by step.

Interactive Sandbox

Expression Calculator

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Practice Problems

18 problems
Problem 1 of 18
Easy
Which equation represents: "A number increased by 7 equals 15"?

Why It Matters

Word problems connect math to real life:
  • 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
The ability to translate situations into equations is one of the most powerful math skills you'll ever learn!

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?

1Try It Yourself

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

From 150+12c=270150 + 12c = 270, write the calculation that gives cc:

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?

2Try It Yourself

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

Km per day = (Total goal - Km so far) / remaining days:

Key Takeaways

  • 1Read the problem carefully and identify what you need to find
  • 2Define a variable (usually xx) 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

Choose the simplest unknown as xx. If the problem says 'one thing is 5 more than another,' let xx be the smaller one, then express the other as x+5x + 5.
Choose the simplest unknown as xx. If the problem says 'one thing is 5 more than another,' let xx be the smaller one, then express the other as x+5x + 5.
Re-read the problem! A negative age or negative count of items means you made an error setting up the equation. Check your translation of words to symbols.
'Twice as much as xx' means 2x2x. 'Three times as many as xx' means 3x3x. The multiplier goes in front of the variable.

Glossary

Variable
A letter (like xx, yy, or nn) that represents an unknown value
Coefficient
The number multiplied by a variable (in 3x3x, 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

sum, plus, more than→+difference, minus, less than→−product, times, of→×quotient, divided by, per→÷is, equals, gives→=\begin{aligned} \text{sum, plus, more than} &\rightarrow + \\ \text{difference, minus, less than} &\rightarrow - \\ \text{product, times, of} &\rightarrow \times \\ \text{quotient, divided by, per} &\rightarrow \div \\ \text{is, equals, gives} &\rightarrow = \end{aligned}

Common English phrases and their mathematical operators

Problem-Solving Framework

Read→Define→Translate→Solve→Check\text{Read} \rightarrow \text{Define} \rightarrow \text{Translate} \rightarrow \text{Solve} \rightarrow \text{Check}

Five steps to solve any word problem

Today's challengeOne problem, three tries

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