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Math Word Problem Solver

Turn words into equations, equations into graphs, graphs into answers

Word problems trip people up not because the math is hard, but because the translation is hard — going from a sentence about tickets and profits to equations like y = 12x and y = 500 + 8x takes a process. Once you have the equations, the graph does the rest.

This lesson teaches that translation process: how to read a problem, spot the unknowns, identify the relationships, write the equations, and then graph them to find the answer visually — no blind formula-plugging required.

The graph starts empty. Type any word problem into the chat — the AI tutor will help you build the model from scratch, step by step, right on the graph.

Graph

FAQ

How do I set up an equation from a word problem?
Start by identifying what you don't know — that becomes your variable (usually x). Then re-read the problem and translate each relationship into math: "costs $12 per ticket" → 12x; "fixed cost of $500" → −500; "total revenue" → y. Write one equation per relationship, then graph both and find where they intersect.
How do I identify the variables in a word problem?
Ask yourself: what is changing? That's usually x. And what do I want to track or find? That's usually y. In a ticket problem, the number of tickets sold changes (x), and the profit or revenue changes with it (y). Label your axes with these quantities before you write any equation.
How do I check that my answer makes sense?
After you read the answer off the graph, plug it back into the original words — not just the equation. Ask: "Does this number make real-world sense?" If the problem says a theater needs to sell 42 tickets to break even, check: 42 × $12 = $504, and the cost is $500 + 42 × $8 = $836 — wait, that doesn't balance! Re-read the problem. This arithmetic check often catches setup errors before they become wrong answers.
What are the most common types of word problems?
Break-even problems (when does revenue = cost?) use two linear equations and find their intersection. Rate/distance problems (d = rt) compare two movers on the same graph. Mixture problems set up two equations about totals and concentrations. Growth problems use linear or quadratic models. The graphing approach works for all of them: build each relationship as a line or curve, then read the answer where they meet.
What does "per" mean in a word problem?
"Per" means "for each" — it tells you to multiply. When you see "$12 per ticket," that means 12 × number of tickets. Similarly, "3 miles per hour" means 3 × hours. Spotting "per" is one of the fastest ways to identify the operation a word problem is describing.
How do I know when to use two equations instead of one?
If the problem has two things changing or competing — like revenue vs cost, or two cars driving at different speeds — you need two equations, one for each. Graph both lines and find where they cross. If there is only one changing quantity (like "how many can I buy with $15?"), one equation is enough.

Related Topics

What is a Function?Slope of a LineQuadratic Equations