Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Word problems have been posed since the earliest mathematics exercises.

Couching an application of mathematical reasoning in terms of everyday objects and activities, the genre of word problems has attracted considerable analysis for education theory over the decades.

It has also garnered a fair amount of parody.

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Find the number of bicycles and tricycles

Help for my son. My math is a bit rusty and I'm trying to remember how to go about answering this question: "There are 3 times as many bicycles in the playground as there are tricycles. There is a total of 81 wheels. What is the total number of…
Rpoe
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Trigonometry - worm thread related word problem

The Question The machine tool diagram shows a symmetric worm thread, in which a circular roller of diameter 1.5 inches sits. Find the amount d that the top of the roller rises above the top of the thread, given the information in the diagram.…
Anna
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How much ketchup is on the table? (Ketchup flow rate problem)

This is a question I came up with while watching my friend squirt ketchup onto his table. He was squirting the ketchup out of a bottle while moving the bottle upwards. A ketchup bottle starts upside down with the tip at the table. Ketchup is…
michaeljan
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What is either player's chance of winning this game?

I came across the following interesting puzzle in a magazine. Suppose we have $101$ suitcases, numbered $0, \dots, 100$, with a bottle of rum in suitcase $x$, and a bottle-opener in suitcase $y$ such that $|x-y|\leq 50$. We have $2$ players playing…
DinkyDoe
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Time-and-Work and Motorcycle Tyres

A problem about motorcycle tyres, related to Time-and-Work or rate-of-work methods. This is not a homework question, nor, as far as I know, a contest question. It is intended as a challenge for Year 10/11 or 15/16-year olds, but should require no…
David Quinn
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Watchdog Problem

I just came up with this problem yesterday. Problem: Assume there is an important segment of straight line AB that needs to be watched at all time. A watchdog can see in one direction in front of itself and must walk at a constant non-zero speed at…
puri
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AHSME Challenge Math Question Cowboy

A cowboy is $4$ miles south of a stream which flows due east. He is also $8$ miles west and $7$ miles north of his cabin. He wishes to water his horse at the stream and return home. The shortest distance (in miles) he can travel and accomplish this…
isaacnewton101
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Translate this logical statement into natural language.

I am trying to translate this logical statement into English: $\forall x(x<10 \implies \forall y(y < x \implies y < 9))$. Note that the statement is true when the universe of discourse is $\mathbb{N}$.The best sentence I could come up with was "all…
Iyeeke
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How to solve 7 blue boxes

I recently came across this problem in a job assessment test. I can't go back and answer the question now, but not knowing the answer is bothering me. Any thoughts on the solution and the means of solving would be excellent. Mary has three…
Rodge H.
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What fraction of finitely presented groups have unsolvable word problem?

What fraction of finitely presented groups have unsolvable word problem? I suspect the answer is "almost all" for some suitable notion, but I can't find any results on the topic. Any references you have would be amazing. Thanks!
HallaSurvivor
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beanstalk doubling every hour what would speed of inchworms need to be?

A beanstalk is continuously growing at a constant rate so that after one hour its length is doubled, after two hours it is four times the original length, after three hours it is eight times as long, and so one. (The growth is uniform: every part…
Randin D
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The Marshal Conundrum

I've thought of a problem which I would like to know the solution to without having to brute force the answer. The Marshal Conundrum About I thought of The Marshal Conundrum after getting the Marshal badge of SFF.SE. I wondered how long it would…
Edlothiad
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The gambler makes 100 bets and wins 10. How much money does he have at the end?

A gambler who makes 100 bets of $1, each at payoff odds of 8 to 1. He wins 10 of these bets and loses 90. How many dollars has the gambler gained overall? I don't seem to understand what "odds of 8 to 1" means. Can someone please explain this to…
Hidaw
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The rich man and the 1000 casks of wine

I recently came across an interesting logic puzzle during a challenge at a programming competition. Neither of the people on the two-person team completing that challenge could figure out an answer that worked in every scenario, and neither could…
Jules
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After adding $10$ cups of water to a container $1/8$ full, it becomes $3/4$ full. What is the volume of the container?

A container is $1/8$ full of water. After $10$ cups of water are added, the container is $3/4$ full. What is the volume of the container, in cups? Ok, I wrote out an equation: $$\frac{1}{8}V + 10C = \frac{3}{4}V$$ I realized that it was asking for…
user265692
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