Writing Equations from Stories

Name the unknown, decide what happens to it, and write what the result equals.

When something is added

"After 7 more, there are 20" is n + 7 = 20.

When there are equal groups

"6 boxes of n pens make 42" is 6n = 42.

Check against the story

Put the answer back into the sentence, not just the equation. It has to make sense.

Define the variable first

Before writing any equation, write "let n be the number of books". Half the difficulty in word problems is losing track of what the letter stands for, and one sentence at the start prevents it entirely.

Find the equality in the story

An equation needs two things that are equal. "Sam spent £20 on 4 identical books" gives 4n = 20. Look for the sentence that says two quantities match — that is where the equals sign goes.

Check the equation against the words

Before solving, read your equation back as a sentence and compare it with the problem. "Four times the price is twenty" matches the story. An equation that solves perfectly but models the wrong situation gives a confidently wrong answer.

Answer in context

The solution n = 5 becomes "each book cost £5". A bare number does not answer a question about books, and stating it in context forces you to check that the number is sensible — a negative or fractional book would signal an error.