Word Problems: How to Turn Words into Equations

Word problems feel hard because they hide the math inside sentences. But they are translation problems: once the words become an equation, the rest is ordinary solving. A fixed method makes that translation reliable.

The five-step method

1. Read the whole problem first. Do not start calculating after the first sentence.
2. Name the unknown. Let $x$ stand for the thing you are asked to find.
3. Translate, phrase by phrase. Turn each sentence into math (see the keywords below).
4. Solve the equation. Use the normal methods — and if it becomes a quadratic, How to Solve Quadratic Equations covers all four methods.
5. Check the answer in the original story. Does it make sense? Wrong answers usually fail this step.

Keywords that tell you the operation

• Addition: sum, total, more than, combined, altogether.
• Subtraction: difference, fewer than, left, remains.
• Multiplication: times, product, of (as in 3 times as many), twice.
• Division: per, out of, ratio, shared equally.
• Equals: is, gives, totals, equals.

Beware more than and fewer than: 5 more than $x$ is $x+5$, not $5+x$ reversed — though addition commutes, the same trap in subtraction (5 fewer than $x$ is $x-5$, not $5-x$) catches many students.

Worked example 1: ages and multiples

Sara has 3 times as many apples as Ali. Together they have 48 apples. How many does Ali have?

Let Ali's apples be $x$. Then Sara has $3x$. Together: $x+3x=48$, so $4x=48$ and $x=12$. Ali has 12 apples, Sara has 36. Check: $12+36=48$. Correct.

Worked example 2: speed and distance

A train travels at 60 km/h for 2.5 hours. How far does it go?

Distance $=$ speed $\times$ time, so $60\times 2.5=150$ km. The keyword per (km per hour) signals multiplication by the time. Check the units: km/h $\times$ h $=$ km. If the units do not work out, the setup is wrong.

Common mistakes

• Starting to calculate before reading the whole problem — the last sentence often changes the question.
• Reversing subtraction and division (fewer than, divided into).
• Skipping the check. An answer that does not fit the story is wrong, even if the algebra was neat.
• Mixing units — convert minutes to hours or cm to metres before solving, not after.

Practice it

Want to check your work? Type the equation you built into the Math Solver and verify each step, or build fluency with similar problems on the practice page. Factoring-type word problems pair well with How to Factor Quadratics Step by Step.