Guides › For students

How to solve math word problems (a method that works every time)

Word problems aren't harder math. They're the same equations with the setup left to you. Most people get stuck before any math happens, so the fix is a routine for the setup.

1. Find the question first

Read to the end and underline the actual question, usually the last sentence. "How many tickets did they sell?" tells you what your final answer has to be: a number of tickets. Everything else in the problem is there to help you get it, or to distract you.

2. Name the unknown, out loud

Write it as a sentence: "Let t = the number of student tickets." Not just "let x =". A named letter stops you mixing up which number is which halfway through.

3. Draw it or put it in a table

A quick sketch, a number line, or a two-row table turns a paragraph into something you can look at. If two things are being compared (two trains, two prices, two people's ages), a table with one row each almost always shows the equation.

4. Translate one sentence at a time

• "is", "was", "will be" usually means =
• "more than" means add, "less than" means subtract (and the order flips: "5 less than t" is t − 5)
• "of" with a fraction or percent means multiply
• "per" or "each" means a rate: something times a count

5. Solve it like any equation

Once it's written down, it's just algebra. Do one step per line so you can find a slip later.

6. Check it against the story, not just the equation

Put your answer back into the words. Can you sell 12.5 tickets? Is the speed of a car 400 miles an hour? If the answer doesn't make sense in the story, the setup is off, even if the algebra is right.

A worked example

A school play sold 200 tickets. Adult tickets cost $8 and student tickets cost $5. They took in $1,240. How many student tickets did they sell?

1. Question: the number of student tickets.
2. Let s = student tickets. Then adult tickets = 200 − s.
3. Table: students, s tickets at $5. Adults, 200 − s at $8.
4. Money: 5s + 8(200 − s) = 1240.
5. 5s + 1600 − 8s = 1240, so −3s = −360, so s = 120.
6. Check: 120 students and 80 adults is 200 tickets. 120 × 5 + 80 × 8 = 600 + 640 = $1,240. It works.

When you're stuck on the setup

Try it with a guess. "If they sold 100 student tickets, how much money is that?" Working one guess through by hand shows you the equation, because the steps you just did with 100 are the steps you'll do with s.