Word Problems

Turn a sentence into an equation, then solve it.

The idea

An algebraic word problem describes quantities in words, and we solve it by translating the description into an equation. The translation, not the solving, is the new skill.

First name the unknown: choose one quantity, assign it a letter, and record in words what the letter stands for — let $w$ be the width in metres. Naming the smallest or earliest quantity usually keeps the other expressions simple.

Next express every other quantity in terms of that letter. Each phrase translates directly: "seven more than the number" is $x + 7$, "twice the width" is $2w$, "three years ago" is $a - 3$. These are expressions, not equations.

Then find the sentence that asserts two quantities are equal — "is", "equals", "sum to". That sentence supplies the equation.

Finally, solve the equation and check the result against the story: a length or an age cannot be negative, and the numbers must make the original sentences true.

Ways to work on it

• Walkthrough. Translate then solve: consecutive integers and an age problem.
• Practice. Translate a random number problem and solve it.
• Hardest. A motion problem: model with distance = rate × time, then solve.

Not sure where to start? Take the ten-question placement test.