Writing Equations from Words

Most word problems are lost in translation, not in the algebra.

A method that works:
1. Write "let x = …" and say exactly what x is, with units.
2. Find the total or the equality — the word "is" usually marks the equals sign.
3. Build each side from the sentence.
4. Solve, then answer in a sentence.

Phrases worth knowing: "more than" and "increased by" mean add. "Less than" means subtract *and reverses the order* — 7 less than n is n − 7. "Of" usually means multiply. "Per" means divide.

The modelling step is choosing a variable and expressing every other quantity in terms of it. When two quantities are related, define one and derive the other rather than introducing a second variable — if two numbers sum to 30 and you let one be x, the other is 30 − x, which keeps the model in one unknown.

Consistency of units is a genuine constraint, not a formality. An equation that adds dollars to hours is malformed regardless of how the arithmetic works out, and checking that every term of an equation carries the same units catches most setup errors before solving.

Finally, the solution of the equation and the answer to the question are often different. If x is the number of adult tickets and the question asks for revenue, one more step remains. Rereading the question after solving is a genuine part of the procedure.