Math word problem
examples with answers
20 fully solved word problems across 6 categories — each with a complete step-by-step solution you can reveal. Filter by type or difficulty to focus on what you’re working on.
“Maria drives from her house to the airport at 55 mph. The trip takes 2 hours. How far is the airport?”
“Two cities are 360 miles apart. Car A leaves city 1 at 60 mph. Car B leaves city 2 at the same time at 90 mph toward Car A. How long until they meet?”
“A cyclist leaves town at 12 mph. A car leaves the same place 30 minutes later at 48 mph in the same direction. How long before the car catches the cyclist?”
“A boat travels 24 miles downstream in 2 hours and 24 miles upstream in 3 hours. What is the speed of the current?”
“A store has 240 items. 15% are on sale. How many items are on sale?”
“James scored 42 out of 60 on a test. What percentage did he score?”
“A jacket costs $180 and is discounted by 30%. Tax of 9% is applied to the discounted price. What is the final price?”
“A population of 12,000 increased by 15% one year and then decreased by 10% the following year. What is the population after two years?”
“A bag contains red and blue marbles in ratio 3:5. There are 40 marbles total. How many are red?”
“A recipe for 6 servings needs 2.5 cups of flour. How much flour is needed for 15 servings?”
“Three partners share profits in ratio 2:3:5. If the largest share is $4,500, what is the total profit?”
“How many liters of 20% salt solution must be added to 8 liters of 50% solution to get a 30% solution?”
“A store mixes $3/lb nuts with $7/lb nuts to make 20 lbs of mix worth $5/lb. How many pounds of each type?”
“Pure acid is added to 40 liters of a 25% acid solution to produce a 40% solution. How much pure acid is added?”
“Worker A paints a fence in 6 hours. Worker B does it in 3 hours. How long does it take them working together?”
“Pipe A fills a tank in 10 hours. Pipes A and B together fill it in 6 hours. How long does Pipe B take alone?”
“A fill pipe fills a pool in 8 hours. A drain empties it in 12 hours. The pool is half full. Both are opened. How long to fill it completely?”
“A rectangular garden has a length of 14 m and a width of 9 m. What is its perimeter and area?”
“A rectangle has a perimeter of 90 cm. Its length is 3 times its width. Find the dimensions.”
“A circular fountain has a diameter of 10 m. A path 2 m wide surrounds it. What is the area of the path only?”
How to use these word problem examples
Each example on this page follows the same structure: a real-world word problem, a complete step-by-step solution, and a reference to the formula used. The goal is to show the full translation process — from sentence to equation to verified answer — so you can recognize the same pattern when it appears in a slightly different form on a test or homework assignment.
For the best results, try solving each problem yourself before revealing the solution. Cover the answer, work through the steps on paper, then compare your method to the worked solution. Differences in method aren’t necessarily wrong — there are often multiple valid approaches — but the underlying formula and verification step should match.
If you have a specific word problem that isn’t covered here, the word problem solver will work through any problem with the same step-by-step format. For the formulas behind each category, see the complete word problem formulas reference.
What makes a good word problem solution?
A complete solution to a math word problem has four components, not just a final number:
- Variable definition — explicitly stating what x (or any variable) represents, with units
- Equation setup — showing the relationship between knowns and unknowns before solving
- Step-by-step algebra — each transition shown and justified
- Verification — substituting the answer back into the original problem to confirm it satisfies all stated conditions
The verification step is what separates a complete solution from a guess that happens to be correct. It’s also the step most students skip — and the one that catches the most errors. Every example on this page includes a verification line for that reason.
Difficulty levels explained
Examples are labeled Easy, Medium, or Hard based on the number of steps required and the algebraic complexity of the setup — not the arithmetic difficulty.
- Easy — one or two steps, single unknown, direct formula application. Typical Grade 6–7.
- Medium — two to four steps, may require expressing one variable in terms of another, or applying a formula in a non-obvious direction. Typical Grade 7–9.
- Hard — multiple steps, system of equations, sequential operations, or a conceptual twist (like sequential percentage changes not being additive). Typical Grade 9–12 and SAT.
Which problem types appear most on standardized tests?
On the SAT Math section, rate & distance problems and percentage problems appear in almost every test. Ratio and proportion appear in both calculator and no-calculator sections. The ACT includes more geometry word problems proportionally. State assessments vary by grade, but mixture and work rate problems typically begin in Grade 9 algebra courses and continue through precalculus. For a complete breakdown of formulas by type, see the word problem formulas page. For a method that works across all types, see the guide on how to solve math word problems.
Frequently asked questions
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