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Word Problem Solver with Steps

Type the story or add a photo. See how the words become equations and an answer.

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Math Word Problem Solver with Steps: Free Algebra Story Problem Calculator

A word problem solver turns a written situation into variables and equations, works through the algebra, then explains what the result means. Math AI Solver helps you follow the translation as well as the calculation.

Words into equations

See the quantities and relationships behind phrases like “twice as many” or “less than.”

Steps you can follow

Move from variable definitions and equation setup to a worked answer with its meaning in context.

Type, paste, or attach

Enter a paragraph or add a clear photo of a printed or handwritten question.

Free to try

Start solving without an account or a paywall on the base answer.

The method

How to Solve Math Word Problems Step by Step

The same three moves work for many algebra story problems: define what you need, translate the relationships, and test the result against the question.

Parse & define

Read the complete question
Identify what needs to be found
Give each unknown a name, such as $t$ for time

Translate & build

Connect the quantities using the story's wording
Pay attention to the order of ‘less than’
Write an equation for each relationship

Solve & validate

Solve the equations step by step
Substitute the result into the original conditions
State the answer with the correct units

Translation key

Word-to-Math Translation Cheat Sheet

Spot the operation, then check which quantity comes first. Small changes in wording can reverse an entire subtraction.

“5 more than a number”

Add 5

x+5

“5 less than a number”

Start with the number, then subtract 5

x-5

“Three times a number, minus 7”

Multiply first, then subtract

3x-7

“A number divided by 4”

Divide the unknown by 4

\frac{x}{4}

“Twice a number is 14”

Set both sides equal

2x=14

Watch “less than.” “5 less than

x

” means start at

x

and subtract 5:

x-5

. It does not mean

5-x

Problem types

Common Algebra Word Problems

These five setups appear often in homework and exams. Define the quantities before choosing a formula.

Distance, rate & time

Use speed and travel time to find distance or meeting time.

d=rt

Mixtures & concentration

Balance the amount of pure substance in each portion of a mixture.

C_1V_1+C_2V_2=C_fV_f

Shared work

Add individual work rates to find how long a job takes together.

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

Age relationships

Describe present ages first, then adjust each age by the same number of years.

f+20=2(d+20)

Geometry stories

Turn dimensions and measurements into perimeter, area, or triangle equations.

P=2l+2w

Worked examples

Word Problem Solutions, Worked Through

Example 1 · Distance and rate

Two cars leave a town in opposite directions at 45 mph and 55 mph. When are they 300 miles apart?

1.Let $t$ be the time in hours. Their distances are $45t$ and $55t$ miles.
2.Add the distances because they travel apart: $45t+55t=300$ .
3.Solve: $100t=300$ , so $t=3$ .

They are 300 miles apart after 3 hours.

Example 2 · Mixture

How much 20% and 50% solution makes 30 liters of a 30% solution?

1.Let $x$ be liters of 20% solution and $y$ liters of 50% solution. Total volume gives $x+y=30$ .
2.Balance the pure ingredient: $0.20x+0.50y=0.30(30)=9$ .
3.Substitute $y=30-x$ : $0.20x+0.50(30-x)=9$ , so $x=20$ and $y=10$ .

Mix 20 liters of 20% solution with 10 liters of 50% solution.

Example 3 · Ages

A father is four times his daughter's age. In 20 years, he will be twice her age. How old are they now?

1.Let $d$ be the daughter's age and $f$ the father's age today. Then $f=4d$ .
2.In 20 years, $f+20=2(d+20)$ . Substitute $4d$ for $f$ : $4d+20=2d+40$ .
3.Thus $2d=20$ , so $d=10$ and $f=40$ .

The daughter is 10 years old and the father is 40 years old.

Common Word Problem Mistakes

1
Reversing ‘less than’
“5 less than $x$ ” is $x-5$ , not $5-x$ . The word order is not the subtraction order.
2
Mixing units
For a speed in miles per hour, convert 30 minutes to 0.5 hours before calculating distance.
3
Answering the wrong question
If you solved for the younger person's age, check whether the question actually asks for the older person's age.
4
Confusing a part with the whole
In mixture questions, 20% of a solution is the amount of pure ingredient, not the total volume.

FAQ

Frequently Asked Questions

Math AI Solver lets you type or attach a word problem and see a step-by-step solution. It explains the equation setup as well as the answer, without requiring a sign-up to try the solver.

Yes. Use the Photo button to attach a clear JPG, PNG, or WebP image of the whole problem. Review the interpreted problem in the result to make sure the numbers and question were read correctly.

Begin with what the last sentence asks you to find. If it asks for a time, define

t

as time in hours. For two unknowns, define each separately or express one in terms of the other before building the equation.

You can enter a scenario with two unknowns and two relationships, such as a ticket-price or mixture problem. Check that the displayed equations represent both conditions before using the answer.

The solution should state what the number means in the story, such as hours, liters, or dollars. Check the units and substitute the answer back into the original conditions.

Yes. You can use Math AI Solver in your browser without creating an account or entering an email address.