Questions tagged [word-problem]
A word problem is an exercise with its main challenge being in translation from words to mathematical concepts and language including symbols and formulas. This tag is not about the unrelated topic in group theory.
1,326 questions
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Why does this method work some of the time (but only some?)
This question showed up in an exam for 11-year olds:
Alice bought some chocolate and vanilla muffins. $\frac{3}{4}$ of her muffins are chocolate and the rest are vanilla. She then bought another 60 ...
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How to Interpret Detection Errors and Compute Performance Metrics for an Autonomous Pedestrian Detection System? [duplicate]
I am analyzing the performance of an autonomous vehicle’s pedestrian detection system, and I want to ensure that I am interpreting the scenario correctly in terms of confusion-matrix components. This ...
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Property of Length Function for Presentation of Group II & Case of Coxeter Group
Let $G$ be a group with presentation $\langle S \ \vert \ R \rangle$. Then any $g \in G$ has (in case $R$ not trivial in general non unique) the form $g=s_1^{a_1}s_2^{a_2}...s_n^{a_n}$ with $s_i \in S$...
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Property of Length Function for Presentation of a Group
Let $G$ be a group with presentation $\langle S \ \vert \ R \rangle$. Then any $g \in G$ has (in $R$ not trivial in general non unique) the form $g=s_1^{a_1}s_2^{a_2}...s_n^{a_n}$ with $s_i \in S$ and ...
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Solving the word problem in hyperbolic groups using Dehn algorithm
Let $G$ be a group with finite presentation $\langle S\mid R \rangle$. For every reduced word $w$ in the free group $F(S)$ denote $|w|$ its length. For every $w \in F(S)$ that
represents the identity ...
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Diophantus Epitaph Riddle
I am trying to solve the Diophantus Epitaph riddle. It goes:
Diophantus's youth lasts $\frac{1}{6}$ of his life. He grew a beard after $\frac{1}{12}$ more of his life. After $\frac{1}{7}$ more of his ...
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A question in the 2025 Vietnamese Matriculation Exam
This question appeared in the Math paper of the 2025 Vietnamese Matriculation Examination. Variations exist between test codes, but essentially the question is as follows:
Allen joins a competition ...
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Linear algebra in two variables word problem
Question: A man was awarded 40 marks in an exam. 3 marks are awarded for every correct answer, and 1 mark is deducted for every incorrect answer. Find the total number of questions in the exam. Had 4 ...
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How do I continue in this confusing algebra word problem?
Problem
In the small hamlet of Abaze, two base systems are in common use. Also, everyone speaks the truth. One resident said, "$26$ people use my base, base $10$, and only $22$ people speak base $...
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I need help solving a time, distance, and speed word problem. [closed]
I would appreciate it if someone could help me with this word problem. I have attempted it myself. and got an answer I do not believe is correct.
Problem: A man runs to a telephone and back again in ...
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How many minutes after the start did Leon and Marko meet for the second time?
Leon traveled at a constant speed from town $A$ to town $B$ and then immediately back to town $A$. Marko traveled at a constant speed from town $B$ to town $A$ and then immediately back to town $B$. ...
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Checking inverse proportion question and how to explain the answer to a GCSE student
Six builders planned to start building a two-storey flat the the
beginning of November, $2021.$ They planned to finish the job by the
end of September the next year. However, for half of their total ...
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Range of addition of $k$ numbers from $\mathbb{N}_n$
In this question from 1989 AHSME stated as follows :
In a certain cross country meet between $2$ teams of $5$ runners each, a runner who finishes in the $n$th position contributes $n$ to his team's ...
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What percentage of the flowers are carnations?
A flower bouquet contains pink roses, red roses, pink carnations and red carnations. One-third of pink flowers are roses, three-quarters of red flowers are carnations and six-tenths of flowers are ...
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Basic Algebraic Word Problem to find dimensions of Rectangular Garden [closed]
A rectangular garden has a length that is 3 meters longer than its width. If the perimeter of the garden is equal to 30 meters, what is the length of the garden?
L = length
W = Width
Here is my ...
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