Math Word Problem Solver

About the Math Word Problem Solver

Most students who get stuck on a word problem are not stuck on the arithmetic. They are stuck on the translation: deciding which number is the rate, which is the time, and what the question actually asks for. This solver makes that translation visible. Its first step always restates the problem as a list of known quantities and the one unknown, so you can see whether the sentence was read the way you meant it.

The tool recognises the problem families that fill most algebra and pre-algebra homework: percent questions (percent of a number, percent change, discounts, tax and tips, finding the original price), distance–rate–time and two travelers moving apart, simple and compound interest, mixtures of two solutions, two people working together, consecutive integers, age puzzles, rectangle and square area or perimeter, and unit price comparisons. Each family has a fixed, exact method behind it, so the answer is computed rather than guessed.

If the wording does not match a family the solver knows, it says so instead of inventing an answer. When the site operator has enabled it, you can then send the text to an AI solver; that answer is clearly labelled unverified because it has not been produced or checked by the exact engine.

What is a math word problem?

A word problem is a mathematical question written as a short story. Instead of $3r = 150$ you read that a car covers 150 miles in three hours. The mathematics underneath is usually a single linear equation or a small system, but it is hidden behind everyday language: "how fast", "how much more", "twice as old", "together".

Solving one has four stages. First, name the unknown and give it a letter. Second, find the relationship the story describes, such as distance equals rate times time. Third, write and solve the equation. Fourth, put the answer back into the story to make sure it makes sense, with the right units. The solver follows exactly these stages and labels each one in its steps.

How to use the Math Word Problem Solver

Type or paste the full problem, including the question sentence. Numbers can be digits or words ("twelve", "twice").
Keep units in the text, such as miles, hours, liters, % or dollars; the solver uses them to choose the right relationship and to label the answer.
Press Solve word problem. Read the first step, "Read the problem", to confirm the known values and the unknown were identified correctly.
Follow the equation and solving steps, then look at the check, which substitutes the answer back into the original relationship.
If you see a message that the wording is not supported, rephrase it closer to a textbook sentence, or try the specific calculator linked in the message, such as the percentage calculator.

Formulas

Distance, rate and time

d = r \cdot t

Rearranged to $r = d/t$ or $t = d/r$ depending on the unknown.

Simple interest

I = P r t

Principal $P$ , annual rate $r$ as a decimal, time $t$ in years.

Compound interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Compounded $n$ times per year; continuous compounding uses $A = Pe^{rt}$ .

Mixture balance

c_1 v_1 + c_2 v_2 = c (v_1 + v_2)

The amount of pure substance is conserved when two solutions are mixed.

Combined work rate

\frac{1}{t} = \frac{1}{t_1} + \frac{1}{t_2}

Rates add, times do not.

Percent change

\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%

Worked example: Speed from distance and time

The example below is solved live by the same engine you use above. The sentence gives a distance (150 miles) and a time (3 hours) and asks for an average speed, so the solver picks the relationship $d = rt$ , substitutes the two known values and isolates $r$ .

Notice that the unit of the answer is built from the units in the question: miles divided by hours gives miles per hour. The final check multiplies the speed back by the time to recover the original distance.

The solution below is generated by the same engine that powers the calculator above.

Final answer

Rate (speed) = 50 miles per hour

How we read your problem

Distance 150 miles, time 3 hours; the rate is unknown. Distance = rate × time; d = 150, t = 3; solve for r

Step-by-step solution

Read the problem
Distance 150 miles, time 3 hours; the rate is unknown.
Identify the known values
Distance = rate × time. Known: d = 150, t = 3. Unknown: rate (speed) (r).
Write the equation
d = r · t
$d = r\,t$
Solve for r
Divide both sides by t: r = d / t
Continue
r = 150/3
Result
r = 50

Formulas used

Distance = rate × time
$d = r\,t$

Substitute the known values into d = r · t and isolate r. Keep units consistent (for example miles, miles per hour and hours).

Verification

Substituting r = 50 back into d = r · t balances both sides ✓

Detailed explanation

How the solver reads a sentence

The reader first normalises the text: number words become digits, "twice" becomes "2 times", percent signs and currency symbols are standardised, and hyphenated measurements such as "12-ounce" are split. It then tries each problem family in a fixed order, looking for the phrases that identify it, for example "consecutive", "years older", "compounded", "liters of a 20% solution" or "per hour".

A family only matches when every quantity it needs is present and unambiguous. If a mixture problem mentions two concentrations but no volumes, the reader does not fill the gap with an assumption; it reports that the problem is not supported. This strictness is deliberate. A confident wrong answer is worse for learning than a clear refusal.

From story to equation

Each family maps to a standard equation. Age problems become a pair of linear equations, for instance "Ann is 4 years older than Ben" gives $a = b + 4$ , and "in 6 years their ages will add to 40" gives $(a + 6) + (b + 6) = 40$ . The pair is solved exactly with determinants, so fractional or negative ages are caught and reported as impossible.

Rectangle problems use $P = 2L + 2W$ and $A = LW$ . When the length is described relative to the width, such as "3 more than twice the width", the reader writes $L = 2W + 3$ and substitutes it, leading to a linear equation for a perimeter or a quadratic equation for an area. Only the positive root of the quadratic is kept, because a length cannot be negative.

Why every answer is checked

After solving, the engine substitutes the answer back into the original relationship and confirms both sides agree. For consecutive integers it adds the integers it found and compares with the stated sum; for an interest problem it recomputes the interest from the principal, rate and time. The check is shown as a step so you can copy the same habit into your own written work.

Some stories have no valid answer: three consecutive even integers cannot add to 75, and a perimeter of 10 cannot belong to a rectangle whose width alone is 6. In those cases the solver explains the contradiction instead of printing a meaningless number.

Common mistakes

Adding times when two people work together. Rates add: if one painter needs 6 hours and another 3, together they need 2 hours, not 9 or 4.5.
Using a percent as a whole number in a formula. A 5% rate is $0.05$ in $I = Prt$ , not 5.
Mixing minutes and hours. Convert 45 minutes to $0.75$ hours before using a speed in miles per hour.
Answering a different question than the one asked, for example giving the sale price when the problem asks for the amount saved.
Forgetting that ages shift for both people. "In 5 years" adds 5 to every person's age, not just one.

Tips

Underline the question sentence first; it tells you which quantity is the unknown.
Write a one-line "let" statement, such as "let $w$ be the width in meters", before any algebra.
Estimate before solving. If a car drives 150 miles in 3 hours, a speed of 500 mph is obviously wrong.
Keep units attached to every number until the end; they catch many setup errors.
If the solver says a problem is unsupported, use the dedicated calculator for that topic, which accepts the numbers directly.

Frequently asked questions

What kinds of word problems can this solver handle?

Percent problems (percent of, what percent, of what number, percent change, discount, tax, tip, original price), distance-rate-time and two travelers, simple and compound interest, mixtures, combined work, consecutive integers, ages, rectangle and square area or perimeter, and unit price comparisons.

Why did the solver say my problem is not supported?

It only answers when the wording matches a family it can solve exactly and every needed number is present. Rather than guessing, it refuses and lists the supported types. Rewording the problem closer to standard textbook phrasing often helps.

Is the AI answer reliable?

The optional AI fallback is only offered after the exact reader refuses, and only when it has been enabled on the server. Its answers are marked unverified because they are not produced or checked by the exact engine, so treat them as a hint and verify them yourself.

Do I have to write numbers as digits?

No. Common number words such as five, twelve or twenty are converted automatically, and words such as twice, double, thrice and half as old as are understood in age and rectangle problems.

Can it solve problems with two unknowns?

Yes for age problems, which become a system of two linear equations, and for rectangles where the length is described in terms of the width. For general systems, use the systems of equations calculator.

Does the solver handle units?

It reads units such as miles, kilometers, hours, minutes, liters, ounces and dollars, converts minutes to hours for speed problems, and labels the answer. It will not compare unit prices given in two different units.

Why is the first step a restatement of the problem?

Most errors in word problems happen during translation. Showing the known values and the unknown first lets you confirm the sentence was read correctly before trusting the algebra.

Turn your next word problem into an equation

Paste the problem above and compare the solver's equation with your own setup before you look at the answer.

Use the Math Word Problem Solver Ask the AI Math Solver