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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.

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What conditions must be present in a word problem to set it up and solve as a system of linear equations (2 variables)?

I was solving various word problems such as mixing solutions, differing interest rates, boat speeds, etc., and I thought what's the common underlying factor among these problems which allow us to ...
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Total fish in a tank

A tank had 20 clownfish and angelfish. 4 clownfish were sold and some angelfish were added to the tank such that the number of angelfish increased by 50%. After that, there were 18 fish in the tank ...
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Number of pupils in the school choir

The number of pupils in the school choir increased by 12% to 56(it seems like this is not a percent). How many pupils were there in the choir at first? My question is, how do I create an algebraic ...
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Math Problem Solving (Super Hard!) [closed]

It is Black Friday and William goes shopping!! He needs to buy the following items: a microwave ($\$50$), a snuggie ($\$15$), his own music album ($\$20$), a Roomba vacuum robot ($\$300$), a limited ...
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1answer
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Expressing using algebra- a wordy question

I am currently practising UKMT questions and this question was from the 1998 IMC. I am struggling to picture how this works. Does the $x$ amount of people behind Wallace equal the $y$ amount of ...
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1answer
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Finding equation from a word problem

Tracy and Kelly take a taxi together so they can split the bill. Since Tracy got picked up first, her share is 4 dollars more than Kelly's share. They also had 2 more charges. They had an airport fee ...
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What is the largest number one can count to using only one's fingers?

When I was in middle school, I remember once discussing with my friends different methods of counting with one's fingers, that is, assigning a numerical value to each finger so one could count the ...
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Three psychologists walk into a bar, each with three unique abilities

Can you help me with this basic permutation problem? Order is important, so any unique order of 'psychologist' and / or 'ability' is counted as one permutation. Here's the problem: Three ...
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Ron and Matt traded postcards. Ron traded half . Matt traded 9. How many postcards did they have before the trade?

I need a simple solution that a 5th grader can understand.Would appreciate your help! Thanks in advance! Ron and Matt both bought postcards during their trip to New Zealand. At the end of the trip, ...
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Number of muffins baked

Mr Ali baked some muffins. (3/5) of the muffins wee chocolate and the rest were vanilla. After she sold (2/9) of the chocolate muffins and (1/2) of the vanilla muffins, 230 muffins were left. How many ...
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What is the orientation of a hypercube in $N$-space needed for a certain projection?

There exists a parallel projection of an $N$ dimensional cube from $N$ dimensional (Euclidean) Hilbert space to the $x-y$ plane whose projected perimeter approaches a circle as $N$ increases. The ...
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Passing Cars problem

Hayden is driving along the Chimpworthy Highway at 100 km/h. He is passed by Elida who is driving in the same direction at a constant speed. Ten seconds after Elida passed Hayden, their cars are 100m ...
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How fast is the river's current?

The twins in the Wammy family often swim upstream $60$ miles to the family's river cabin. Tammy takes $5$ hours longer to swim upstream to the cabin than she does to return. Sammy takes $9$ hours ...
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Number of chocolate chip and butter cookies

(3/5) of the cookies were chocolate chip cookies and the rest were butter cookies. After (2/5) of the chocolate chip cookies were sold, there were 24 more butter cookies than chocolate chip cookies. ...
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1answer
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Monthly allowance spent

Devi spent (2/3) of her monthly allowance on food and (5/6) of the remaining amount on stationery. She spent $35 more on food than on stationery. How much as Devi's monthly allowance? My work: ...
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Half-Life of a drug

The half-life of a certain drug is 5 days. That is, 50% of the drug has left the body after 5 days. Let's say someone takes 305 mg of this drug once every 5 days. How many mg of the drug remains in ...
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Minimal rotational degrees of freedom needed in N-space

How many rotational matrices are needed in N-space to achieve an arbitrary attitude when allowed to be successively applied? Each N by N rotation matrix will allow only a rotation in a plane, so only ...
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1answer
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8 cleaners clean an office block in 3 hours…

I am stuck on this question style my teacher gives me each week. I have no idea to answer it and it hurts my brain! Please would you give some time to help me and walk me through this question: 8 ...
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1answer
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Probability question with no number

I Ama trying to solve this probability question but it does not indicate the total amount of socks in the drawer so I am not sure how to go about solving it. Peter has many socks, all the same except ...
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Is there a non-Abelian algebra such that sequences can be 'reconstructed' given constraints?

Disclaimer: I'm a software engineer trying to use mathematics to solve a problem. I only have a shallow understanding of (abstract) algebra. My terminology will probably be wrong. Please be gentle. I'...
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How can I construct equation for this? And solve [closed]

Joseph is 7 times as old as his daughter, In five years times he will be 4 times as old as daughter will be then, what is their ages now?
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Inverse Variation Problems

The cost of stainless steel tubing varies jointly as the length and diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00, how much will a 9 foot length with diameter 5 inches ...
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Safe following distance calculation

Two cars are stopped at a light. Car A is in the front. Car B is right behind it. Distance between is zero. Both cars are stopped. The light turns green. Car A accelerates at constant rate of 1. ...
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$42$ (U.S.) coins make $\$1$. If there's at least one quarter, dime, nickel, and penny, find the number of dimes and nickels.

My piggy bank has $42$ coins worth exactly $\$1.00$. If it has at least one quarter, dime, nickel, and penny, find the total number of dimes and nickels. I found $1+ 5 + 10 +25 =41$ cents with the ...
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Need help in finding my mistake in one fraction/percentage word problem

Question : Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10% more stamps than Jennifer. How many stamps did Jennifer begin with ? ...
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Ant crossing plane

A rectangular 12 cm by 20 cm waffle is divided into 1 by 1 cm squares. An ant crawls along a straight path from one corner to the opposite corner. How many squares of the waffle does the ant cross ...
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Ratio of the number of English and Chinese books

In a library, the ratio of the number of English books to the number of Chinese books was 8:5. After the librarians bought 50 more Chinese books, the ratio became 4:3. a) How many English books were ...
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Ratio. Number of sheep and chickens

At a farm, the ratio of the number of chickens to the number of sheep was 5:2. After the farmer sold 15 chickens, there was an equal number of chickens and sheep. How many chickens and sheep were ...
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Primary 6a and 6b collected from a charity

The ratio of the amount of money Primary 6A collected to the amount of money Primary 6B collected from a charity sale was 4:5. A pupil from Primary 6A donated $6 more than the ratio because 7:8. How ...
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Word problem I can't solve

Hello I have been trying to solve this math word problem, I tried drawing a diagram and I came to the answer 2 but I am not sure about my answer and would appreciate some help Thanks! Here is the ...
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1answer
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Probability of two people meeting given that one arrivas at a specifc time

I was just wondering if someone could maybe check my logic of working this question out. As a disclaimer I realise that there is questions of similar nature on the forum but, I have not looked due ...
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1answer
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Solving a “How many coins of each type do I have?” word problem with linear algebra and MatLab command line

The coins currently in Canada are nickels (worth \$0.05), dimes (worth \$0.10), quarters (worth \$0.25), loonies (worth \$1.00), and toonies (worth $2.00). The coins I have in my pocket have a ...
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1answer
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How many times harder must one dog be pulling?

A sled is pulled forward by two dogs, each attached to the sled by a tow line. The angle between the two tow lines is $35^\circ$. How may times harder must one dog be pulling if the sled's path is at ...
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Ratio and Proportion Maths Problem Solving

A jar contains some cookies. The weight of the jar and cookies is 700g. Meghan eats $\frac{4}{5}$ of the cookies. The weight of the jar and cookies is now 400g. How much does the jar weigh? How many ...
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1answer
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How much time elapses by which time a thief has a $50\%$ chance of success in opening a combination lock?

So I am not entirely sure I have approach the question correctly and at first I thought it to be pretty straight forward but there is something in the wording of the question that make me think there ...
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1answer
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The width of a pavement around a building is uniform. The pavement is equal to 8500m$^2$ and the building is 120m by 80m.

The width of a pavement around a building is uniform. The pavement is equal to 8500m$^2$ and the building is 120m by 80m. What is the width between the building and pavement? I mapped it out and I ...
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3answers
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A rectangular lot has a perimeter of 44cm. The area of the lot is 107cm$^2$. Find the dimensions of the lot?

I'm in grade 11 math. I need help to solve this. A rectangular lot has a perimeter of 44cm. The area of the lot is 107cm$^2$. What are the dimensions of the lot? So far I did this but it doesn't ...
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Find the distance traveled if the velocity is given. I want to confirm my reasoning

I wanted to make sure about something. My velocity function is given as $ v(t)=e^{-kt}$ for some fixed k>0. I am asked to find the distance traveled from t=0 to t=10 if the initial position is at x=0. ...
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Calculus Problem concerning Work

I came across a question in my calculus book that asked me to calculate the work done my gravity in pulling a mass of $100$ pounds from a height of $500$ miles above the earth to the surface of the ...
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1answer
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Tetrahedal dice, biased and un biased

Question Two tetrahedral dice, both numbered 1 to 4 are tossed. If one die us a fair and the other biased so that a four is twice as likely as any other score, setup the possibility space and use ...
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Word Problem - Linear distance in terms of a walking velocity and a second driving velocity

Every day I pick up my son from the bus stop at $4:00$ PM and go home. One day he started walking (towards home), leaving school at $3:30$ and I met him at some point in between. We arrived home $10$ ...
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Speed, Distance and Time GCSE Physics Question. Help please…

It takes me 20 minutes to walk from home to the bus station. I catch the bus from the bus station to work each morning. My bus journey is 10 miles and usually takes 30 minutes. I can catch a bus at 20 ...
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Basic algebra word problem: Number of sheep?

A farmer raises sheep and chickens at his farm. The number of sheep is $\frac{1}{3}$ the number of chickens. There are $96$ fewer sheep legs than chicken legs. How many sheep are there at the farm? ...
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Calculating Weapon Reload with Wind-up

A game I play has a weapon that has a "wind-up" feature, where the reload time decreases the more times it's fired. I'm curious as to how to calculate the amount of time it will take to get to the ...
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How can I find the ages of the people in a word problem involving family ties which seems intricate?

The problem is as follows: Marvin is the only son of Jennifer's grandfather, and Lindsey is the only daughter-in-law of Marvin's grandfather. If the only children of Jennifer are twins of 7 years of ...
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What does the pronoun “they” refer to in this sentence “in how many ways can they select the host for these championships” [closed]

I am reading a textbook on statistics. There is confusion about a paragraph in an exercise. If the NCAA has applications from six universities for hosting its intercollegiate tennis championships ...
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age-based word problem

Peter's age is three years more than three times his son's age. After three years, Peter's age will be ten years more than twice his son's age. What is Peter's present age? I have tried to put this ...
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Need guidance solving this particular propositional logic question

I've been trying to get my head around this logic question posed on an exam I took some weeks ago, but wasn't able to figure it out by myself, so I've come here for some help. The question reads as ...
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1answer
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What recommendations can be used to speed up solving a logic puzzle problem involving placing in order a set of elements using a logic grid?

The problem is as follows: A group of archaeologists found an artifact to which they believe tells an account of the results of a race in an ancient Hippodrome. After days of studying the ...
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algebra word problem help

A man has a stack of blank DVDS. on day one he uses one third of the DVD's. on day 2 he uses half the DVD's that were left from day one. At the end of day 2 there are 12 DVD's left. how many DVD's ...