Word Problems
Supported Types of Word Problems
- We only solve word problems that lead to equations, inequalities, and systems of equations.
- We focus on solving word problems at elementary and high school levels with moderate difficulty.
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Supported Types of Word Problems:
- Word problems on direct and inverse proportionality (and their combinations)
- Word problems on motion
- Word problems on collaborative work
- Word problems on mixtures and solutions
- Word problems on sequences (arithmetic, geometric)
- Word problems on sets (Venn diagrams, Cartesian product)
- Word problems on combinatorics
- Word problems involving geometric calculations (perimeters, areas, volumes, etc.)
- Word problems on extrema using derivatives
- Specific problems (age, LCM, GCD, percentages, scale, clock hands, etc.)
- General problems
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Supported Types of Mathematical Operations:
- Word problems leading to a linear equation
- Word problems leading to a linear inequality
- Word problems leading to a quadratic equation
- Word problems leading to a system of equations
- Word problems leading to an exponential equation/inequality
- Word problems leading to a trigonometric equation
- And more
- View a Live Example
Advantages Over Standard AI Tools
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Some of the key benefits include:
- We have added hundreds of methods and knowledge enhancements that increase the chances of successful problem-solving.
- More structured and clear solutions.
- More efficient and detailed equation, inequality, and system solving.
- Every step of the process is thoroughly explained.
- Interactive mode - helps students better understand the problem text, relationships, and equation formulation through a set of targeted questions focusing on common student mistakes.
- No monthly subscription – pay only for what you need.
- We have spent hundreds of hours optimizing solutions for the best possible results.
Limitations
- Although we achieve over 90% success in solving word problems (based on empirical testing), we cannot guarantee that every problem will be solved correctly.
- This is due to the fact that even the best modern LLMs (large language models) used for text analysis are not flawless (despite incorporating additional know-how).
- For example, the success rate for solving problems in the book Mathematics – Preparation for Graduation and University Entrance Exams by Jindra Petáková is approximately 95% (based on a set of 20 problems).
- The presence of LLMs in text analysis and equation formulation introduces some level of non-determinism. Thus, outputs may vary over time (even though both responses can be correct).
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The difficulty of a problem is challenging to define, as it depends on various factors, such as:
- Linguistic complexity – text length, structure, vocabulary, clarity of wording (ambiguity, complexity)
- Mathematical complexity – number of mathematical steps, types of operations, level of abstraction
- Logical complexity – number of conditions, complexity of logical relationships (temporal sequences, dependencies)
- Problem formulation – presence of irrelevant information
- Context of the problem
- And more
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Recommendations for Solving Word Problems:
- Always input only one problem at a time.
- If the problem contains subquestions, there should be no more than three.
- We do not solve problems that do not directly lead to equations/inequalities/systems – such as construction problems, proofs, graphical (illustrative) problems, enumeration, etc.
- For photo submissions, printed input is ideal. Handwritten submissions have a lower success rate (depending on handwriting style), so checking and adjusting the problem before submission is recommended. Alternatively, the problem can be entered manually or copied.
Technical Solution
We have designed a clear and simplified framework that demonstrates how we effectively solve word problems. Our solution offers several advantages:
- Problem classification allows us to incorporate specific knowledge and methods that significantly increase the chances of solving the problem successfully. For more complex problems, we even perform a preliminary analysis.
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Structured approach unlike the unorganized flow of information with ongoing corrections offered by current LLMs, our method ensures a clear and well-thought-out format.
- Introducing unknown variables
- Problem breakdown (analysis)
- Defining the problem's objectives (what is being asked)
- Equation formulation with explanations
- Detailed step-by-step solution of equations with explanations of each operation
- Verification of results against conditions
- Calculation of final objectives
- Conclusion of the word problem
- By generating structured data as output, we handle all calculations, including final results. This ensures that:
- Equation and system solving is error-free, allowing us to successfully solve even the most challenging problems where pure LLM-based approaches fail. Most models rely on Python libraries that cannot handle complex equations/systems.
- Each equation, system, and mathematical transformation is explained step by step in full detail – something that standard LLMs do not offer.
