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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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Is it possible to know the result of a match between three teams with only knowing their goals for and goals against?

I've found this problem in my book and left clueless on how to make the right interpretation to come up with a solution. The situation involves a hockey match. Typically when you have a goals for and ...
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How to do the computation to find the number of coins in a chest if there are different denominations?

This problem has left me going in circles, since I don't know how to relate the number of coins and denominations to obtain a maximum quantity. Does this problem requires the use of derivatives?. If ...
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How can I determine the maximum profit in a problem involving inequations in both sides?

Needless to say that what I've already tried it didn't work hence I'm requesting assistance on this. Overall I want to know if there is some graphical approach on this problem. Can this be expressed ...
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Precalculus Composition of Functions Question

The prompt: Amparo bought a jacket with a \$50 gift certificate she received as a birthday present. The jacket was marked 33% off, and the sales tax in her area is 5.5%. If she paid $45.95 for the ...
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Does a problem involving finding the least amount of trials in weighing to reach a certain quantity can be solved without derivatives?

I've been going in circles with this kind of problem, hence need some help into trying to find if this kind of situation can be solved without the use of derivatives. The problem is as follows: In ...
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Fibonacci's sequence to calculate growth of a family

I'm trying to solve the following mathematical dilemma: On the 1st of July 2000 a Lizard bears 4 babies. On the 1st July 2001 each of those Lizard bears in turn 4 babies. And so on. Assumed that ...
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How to find the least number of containers required to fill up a certain quantity?

I'm still stuck on this problem involving finding the least number of bottles. I am not sure whether if this problem belongs to combinatorics or maybe does it has to do with greatest common divisor or ...
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How to find the number of machines given a set of rental prices?

I'm stuck in a situation involving rental. Typically I would assign a set of constants based on their price but I'm confused on how to use it or if it applies here. The problem is as follows: A tv ...
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Particle on a line question with integrals calc2

I have a question for calculus two regarding a particle on a line. Question: A particle moves along a line with acceleration $a(t)=−1(t+3)~2\text{ft}/\text{sec}^2$. Find the distance traveled by ...
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Does there exist a way to simplify or build a table to find the truth in a set of given statements involving 5 individuals?

This problem has got me going in circles for several hours and I'm not sure what to do, the problem is as follows: At a semiconductor laboratory in Hsinchu a security guard caught five ...
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Word problem regarding finding torque of a shoulder

Question: What is the torque about the shoulder if the arm is held in an abducted position at 60 degrees from the body in the frontal plane while holding a 10 kg dumbbell? Assume that the mass of the ...
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Need help with a survey word problem…

I am unable to solve this problem in attached screen shot and need help
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Forming a constrained optimization from a given problem?

A workshop produces a product out of three infinitely divisible ingredients X, Y , and Z. The ingredients cost p, q, and r pounds per kg, respectively, with p, q, r > 0 all different, and the factory ...
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How can I form the equation in this word problem?

A rectangular garden measures 20m by 80m ,A large path of uniform width is to be added to along both shorter sides and one longer side of the garden.The landscape artist doing the work Want to double ...
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please explain if the following question is correct or not; if it is incorrect, how it can be saved?

A boy starts from his home at a certain time with a certain speed to pick up his girlfriend from the office at 5 pm. One day his girlfriend left the office at 3 pm and start walking to home with a ...
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Why the number of pints is proportional to the square of the height of a statue?

The main question: If 1 pint of paint is needed to paint a statue 6 ft. high, then the number of pints it will take to paint (to the same thickness) 540 statues similar to the original but only ...
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Cardinality of set of words [duplicate]

How can we prove that for the countable alphabet $A$ the cardinality of set of all finite words over this alphabet $A^*$ is equal to $\aleph_0$
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Just for fun word problem.

You have 10 chickens. Each chicken lays an egg every 10 seconds. It takes 100 days for an egg to hatch and begin laying eggs, then 50 more days for it to die. After 10 years how many chickens would ...
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Finding Area for Related Rates Ladder Question [closed]

A 52-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by ...
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A game awards either $7$ points or $4$ points at a time. How many possible total scores can never be reached if the game is played indefinitely?

In the Martian game of QZX. a JBL is worth 7 points and a KMD is worth 4 points. There is no other way to score. Games can continue indefinitely. How many positive integer scores can never be reached? ...
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Working out the final velocity of an object

Okay, so I was working out the final velocity of an object but it came out way too high. Just wondering if there was a slight error in my calculations. I've linked my working out in the image using MS ...
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Is “three ten-millionths of an inch” the same as “thirty millionths of an inch”?

I was reading this article when I came across a fraction that was difficult for me to comprehend: three ten-millionths of an inch I thought to myself that wouldn't this be the equivalent of: ...
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Confused by a seemingly too simple solution for inequality word problem

Between a city and a village lie two bike tracks: 35km of paved road, and 20km of dirt road. Because of the thick forest between them, a cyclist can choose to ride only one. The speed on the ...
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Trigonometry Modelling

I have another question I'm stuck on and have literally no clue to start. It's to do with trigonometry and bearings and I am horrible at worded questions. "A jet ski travels 200m in a straight line ...
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proving that an arithmetic sequence is equal to a geometric sequence

how can I prove that an arithmetic sequence is equal to a geometric sequence if and only if the initial values of the sequences are the same and the common difference of the arithmetic sequence is 0; ...
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A and B can do a job together in 80 days, B and C in 20 days.

A does the job for 5 days, then B comes over and does it for 15 days, then C does it for 18 days and the job is finished. How much time does C need to do the job alone? Attempt: Let their job ...
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What's a quick method of solving this type of question?

Two points A and B are 200M apart. Two lions are at the opposite ends when they start running towards the other point with speeds 18km/hr (lion at point A) and 36km/hr (Lion at point B) respectively. ...
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Help solving a digit and word code problem/riddle: sum of four “ONE”s is “TEN”

Replace each letter by a digit. The same digit must represent each letter, and no beginning letter of a word can be zero. No two letters can be the same number. Find the digits represented by the ...
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Mixing two different essential oils to their maximum safe dilutions in one carrier oil

I want to mix cinnamon bark essential oil (safe at a maximum 0.5% dilution) with tea tree essential oil (safe at a maximum 15% dilution) in shea butter. Shea butter is safe undiluted. The above ...
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1answer
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Why is my solution to this particular word problem incorrect?

I have a situation with 3 cars: A, B, and C. Cars B and C start at the same spot, while car A is already 15km ahead: The velocities of the cars are: $V_A = 50km/h$ $V_B = 40km/h$ $V_C = 60km/h$ ...
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40 views

Find the unit price of each item which was paid as whole

I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is: Three friends go into a book shop. Salma buys a cook book and a novel, she pays \$ ...
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Word problem about a diminishing military contract?

Here's a question I've had a bit of trouble answering: A military member is assigned $5$ years to serve abroad. For each month they serve in which they have exemplary behavior though, $10$ days is ...
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1answer
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Pyramid Of Spheres

A collection of identical spheres can be formed into a “square” pyramid (a pyramid with a base (bottom layer) made up of $n \times n$ spheres whose next layer is made up of $(n-1) \times (n-1)$ ...
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Alternative words for “parts” of a bi-partite graph

Perhaps the most common term for each of the two disjoint sets in a bipartite graph is "part". So I can say for example: One "part" of the $K_{4,4}$ connects to a corresponding "part" of a ...
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Age, Ratio word problem

A is x years old. In 4 years time his brother B will be 3 times as old as him. Find the age of B in 4 years time.
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Number of oranges left [closed]

At a fruit stall, $40\%$ of the fruits were oranges and the rest were apples. After some oranges were sold, the number of oranges became $20\%$ of the total number of fruits remaining. There were $120$...
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Suppose a pizza has 4 slices, and each slice can be topped with either peppers, onions, or both. How many different pizzas can be made?

Suppose a pizza has 4 slices, and each slice can be topped with either peppers, onions, or both. How many different pizzas can be made? I am using Burnside's counting theorem with the group $G=\left \...
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1answer
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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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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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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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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: ...