What is Word problem: Definition and 499 Discussions

In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.
Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.

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  1. C

    Write a realistic word problem for which this is the correct equation

    So far for the word problem I have: A 100 g particle, traveling at 40 m/s, collides inelastically with another 100g particle traveling towards it at 30 m/s. Now from the equation provided we need the question to ask us to find delta t, and that's simple enough but I'm not sure what that 1/2 is...
  2. drooble122

    Confusing algebraic word problem

    I have great difficulty understanding the solution. I'll go through it line by line: c boys can mow a acres in b days. This condition is from the problem and I understand it. 1 boy can mow a acres in bc days. Why not b/c days? After all isn't 1 boy from c/c=1? n boys, or 1 man, can mow a...
  3. M

    How should I solve this Diophantine equation word problem?

    Proof: Let x be the number of men, y be the number of women and z be the number of children. We need to find the solutions in the non-negative integers for the Diophantine equation 3x+2y+0.5z=100 such that x+y+z=100...
  4. M

    Can anyone please verify/check if there's error in this word problem?

    Proof: Let x be the number of dollars and y be the number of cents in the check. Then we have 100y+x-68=2(100x+y). From the hint, we get the following Diophantine equation: -199x+98y=68. Applying the Euclidean Algorithm produces...
  5. This Is Me

    Unanswered: Unraveling the Mystery of Extended Thinking

    This is an extended thinking portion in my textbook, and I would really like to know why this is. I'm not too sure what the answer to this is, and unfortunately, there is no answer to extended thinking in my textbook. I've been trying to figure this out for some time now and I'm completely stumped.
  6. C

    Using a Problem Solving Technique for a simple word problem

    Summary:: I have a document which was written by previous tutor supervisor/instructor at my undergraduate school. I want to learn how to use this technique for other math/physics subject besides algebra... I will provide an example of how to use this technique. I found an old textbook (College...
  7. harpazo

    Age Word Problem Involving Ratio

    The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them. I never saw an age problem involving a ratio but let's see. Abraham to Adam = 5 : 7 Let x = present age of Abraham and Adam. Age of Abraham = 5x...
  8. pairofstrings

    B Converting Word-Problems into Equations and Vice Versa

    Hi. Can every word-problem be converted into equation? Can every equation be converted into word-problem? Thanks!
  9. L

    MHB What is the correct formula for calculating savings plan?

    Hello! I am having trouble with this question. Please look at the image. I understand that I’m supposed to use the A = p *(1 + r/n) [(1 + r/n)n*y - 1] / (r/n) formula but I’m really stuck on this problem.
  10. N

    How to Solve a Trigonometry Word Problem Involving Distances

    The sketch: First of all find the length of PQ on i.e $$4 \ inches - 1 \ mile$$ $$1.2 \ inches - x \ mile$$ $$x = \frac{1.2}{4} = 0.3 \ mile = 1584 \ ft$$ Now, I do not understand where shall I draw the horizontal, and the connection between the lengths of the contours, so I'll be grateful if...
  11. N

    Trigonometry - Cricket related word problem

    Hello, I don't know anything about cricket, so I'll be grateful if you help me with constructing a diagram for this problem. Here's my attempt. I looked up on the internet and I pretty much get the idea of pitches and wickets, but still cannot connect everything together. Thank you.
  12. N

    Trigonometry - Horizon Related Word Problem

    Hello! I'm trying to solve this problem. Here's the diagram I tried to make. I have difficulty understanding this math problem.. I've tried to solve the problem using the symmetry of the triangles but I didn't get the right answer, and I can't seem to understand the "concept" of the horizon...
  13. M

    MHB Word Problem for slope intercept graph equation

    I have this word problem that is asking for two different answers, the equation for the data and to calculate the shipping rate. I'm not understanding how to address either of the questions. Will someone please help me with this answer?
  14. Mr Davis 97

    Algebra word problem about planning a concert

    This seems like a simple problem, but I am a little confused by a few things. For one, what is the use of the piece of information that when they charged $100 per person they got 3000 people to come? Also, how should I proceed with the information "for every $2 decrease in price they would have...
  15. L

    Physics Graph Word Problem -- Motion of a person skiing down a slope

    I was able to do the first graph knowing that acceleration is 9.8 and my distance goes up by 10s (y-axis) and my time goes up by 1s (x-axis). For the other 3 graphs, I'm not sure where to begin because I don't know how to figure out my velocity
  16. A

    MHB Word problem for winning percentage

    In an inter school basketball league, the team from Brent International School has won 12 out of 25 games, a winning percentage of 48%. We have seen that they need to win 89 games consecutively to raise their percentage to at least 60% . What will be their winning percentage if they win; a. 10...
  17. J

    MHB Real Estate math word problem help

    I am studying to take a real estate exam. I am having problems determining the correct formula on the percentage problems. I need help solving the answer and understanding the correct formula. Help is much appreciated. The math problem is: The subject is a mixed use undeveloped property with 3...
  18. K

    MHB Algebra word problem solve for x

    Help me solve this word problem please & explain how you did it-thanks so much, I 'm tearing my hair out. Jason purchased a can of tomato sauce and three pounds of apples for $\$7.05$. Gina purchased a can of tomato sauce and 5 pounds of apples for $\$11.35$. What is the price of the tomato...
  19. L

    MHB Introductory Algebra Percentage Word Problem

    The problem as given in the book: The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price? All I could think was trying to work...
  20. karush

    MHB 2.2.294 Euler's method word problem

    George makes a paper boat with his brother Bill and goes out in the rain to play with it. It falls in the stream along the curb, racing towards the sewer. Let t be measured in seconds, p be the velocity of the paper boat in meters/second and g be George’s velocity, measured in meters/seconds...
  21. S

    MHB Fraction word problem: how many rows are devoted to each plant

    2. Betty would like your help planning her garden whose rows are all of equal length. She would like to grow carrots, beans, sunflowers, tomatoes and peppers. She tells you she would like to devote twice as many rows to growing peppers as she does to beans. She only has enough tomato plants to...
  22. R

    MHB High school simple algebra word problem

    The 100W light bulb (cost 0.60 dollars) is not going to be used anymore and is being replaced with the 20W (cost 3 dollars) low energy light bulb. If electricity is charged at $0.15 per kWh, for how many hours must the low energy bulb be used in order for the lower cost of running it to exactly...
  23. M

    MHB How Do You Determine the Joint CDF for Joy and Ethan's Arrival Times?

    So I have this word problem as seen below: Joy and Ethan have agreed to meet for dinner between 8:00 PM and 9:00 PM. Suppose that Ethan may arrive at any time between the set meeting. Joy on the other hand will arrive at the set meeting under the following conditions: • Joy will always arrive...
  24. T

    Python Finding the day from a given date

    The question is as follows : ''Given that January 1st, 2018 is a Saturday, write an algorithm to determine the day of the week for a given date provided as an input. The input to the algorithm should be in the format YYYYMMDD, where March 21st 2018 is written as 20180321'' My issue is as...
  25. F

    MHB Truck Height Limit for Ellipse Overpass: 40ft Wide, 15ft High

    The question asks, "A one-way road has an overpass in the form of a semi-ellipse, 15 ft high at the center, and 40 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can pass under the overpass?" I don't think this is a super complicated question yet it proves to be too...
  26. M

    MHB Solve Algebra Word Problem: Overpayment Amount of \$85.00

    March bill was \$400.00 for 25% to be paid of that. There is a recurring overpayment amount of \$85.00 so \$85.00 was to be withdrawn from the 25% of \$400.00 for a total of \$15.00. \$400.00 x .25 = \$100.00 \$100.00 - \$85.00 = \$15.00 However, rather than doing that; the following was...
  27. T

    Relative Velocity of Swimmer: How to Calculate Total Time for Different Paths?

    So I was just wondering if someone could check my method for (b) as sometimes I can have a tendency of getting the relative components wrong ect. Diagram 1 (a) Time for PY: ##T=L/c## Time for YP: ##T=L/c## Total Time:##2L/c## (b) Velocity for PY: ##c-v##...
  28. T

    Why Does My Relative Density Calculation Not Yield a Numerical Value?

    So I am a bit stuck on this question as my result using the above equations dose not give an numerical value which I assume from the question is needed. So here my method for solving My first thought was that if on the planet the person can throw a rock 10 time further then that it implies in...
  29. J

    MHB Ratio word problem: What fraction of the original counters remain in the bag

    I have a word equation i cannot figure out! anyone have any ideas? There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the...
  30. alijan kk

    Solve Word Problem: 30 Persons in 4 Days = 40 Persons in x Days

    A task is completed by 30 persons in 4 days. In how many days, the same will be completed by 40 persons ? My attempt: (30/4)/1=(40/x)/1 (30 persons per 4 days per task=40 persons per x days per task) Doing this way i found x= 5.33 day or 5 whole days . is this correct way of doing this problem?
  31. Charge

    Adding Vectors to Find Velocity

    Problem: Dr. L and his cat Kepler are coming home from fishing. They ended their trip on the south bank of a river, directly across a 1200 m wide river, from where Caroline was going to pick them up on the north bank. They are in identical boats that can travel at 4 m/s (Vb). The river is...
  32. opus

    Simple Unit Conversion Word Problem Help

    Homework Statement During a heavy rain, a section of mountainside measuring 2.5 km horizontally, 0.80 km up along the slope, and 2.0 m deep slips into a valley in a mud slide. Assume that the mud ends up uniformly distributed over a surface area of the valley measuring 0.40km x 0.40km and that...
  33. T

    I Truth, lie and random confusion

    So I am very, very new to logic based questions, and in the past have solved some with relative ease but whilest scrolling through the next to find some example stuff I came across a website that gives a question and hints to the question if stuck, so I thought this would be good practice. But...
  34. J

    MHB Can you calculate the total mass of three parcels at a post office?

    At a post office, there are three parcels of different masses. The mass of the first parcel is y grams. The mass of the second parcel is 500 grams greater than that of the first parcel. The third parcel is 210 grams lighter than the first parcel. a) Find the total mass, in grams, of the three...
  35. J

    MHB Age word problem: when john is 12 years old, how old is his mother?

    John is x years old and his mother is 25 years older than he is. a) How old is John's mother? My answer: x + 25 = mother b) What is the sum of their ages now? my answer: x + mother = current age c) when john is 12 years old, how old is his mother? my answer: 12 + 25 = 37.
  36. alijan kk

    Age Word Problem: Find Father & Son's % Difference

    Homework Statement If a father is twice as old as his son. six years ago father was thrice as old as his son. Find the percentage. A.10 B.12 C.120 D.6 Homework EquationsThe Attempt at a Solution first i am trying to express the equation f=age of father s=age of son f=2s (father is twice as old...
  37. opus

    Constructing accurate diagrams of word problem- Trig

    Homework Statement A canoe is floating down a creek. The canoe is first spotted 80 feet away. 7 minutes later the canoe is 45 feet away, making a 40° angle between the two sightings. How far did the canoe travel? Homework Equations Law of Sines and Law of Cosines The Attempt at a Solution...
  38. G

    MHB How to Solve a Vector Word Problem Involving Airplanes and Wind?

    An airplane is flying on a bearing of South 27degrees West at 485 mph. A 35 mph wind is blowing from a direction of South 72degrees East. What is the actual bearing of the plane and the ground speed of the plane? I've been stuck on this problem for so long and am going to ask for help
  39. R

    Calculus derivatives word problem

    Homework Statement Is it possible to accurately approximate the speed of a passing car while standing in the protected front hall of the school? Task: Determine how fast cars are passing the front of the school. You may only go outside to measure the distance from where you are standing to the...
  40. opus

    Population drop word problem -- help with the Algebra please

    1. Homework Statement You’re testing the effect of a noxious substance on bacteria. Every 10 minutes, one-tenth of the bacteria which are still alive are killed. If the population of bacteria starts with 10^6, within which period of 10 minutes will 70% of the bacteria be killed? Homework...
  41. M

    Shoot a basketball with a minimum speed at some angle

    Homework Statement You should shoot a basketball at the angle ##\theta## requiring minimum speed. Avoid line drives and rainbows. Shooting from (0, 0) with the basket at (a, b), minimize ##f(\theta)= 1/(a \sin (\theta) \cos (\theta) -b \cos^2 (\theta))##. (a) If b =0 you are level with the...
  42. phantom lancer

    Physics Word Problem: Arrow and moving target collision

    Homework Statement Find the 2 unknown variables.[/B]Homework Equations Am I doing this right? Can someone help me find the solution?[/B] The Attempt at a Solution To compute for the velocity of the target/arrow combination immediately after the collision: M_bV_{bi}=M_bV_{bf}+M_wV_{wf}...
  43. R

    Creating system of equations from word problem optimization

    I have this word problem, and was wondering how I would go about creating a system of equations. Here is the question: Problem: You are a small forest landowner, and decide you want to sustainably harvest some of timber on your property. There are costs related to the infrastructure needed to...
  44. E

    MHB Solving an Investment Word Problem

    So I have an investment word problem that I have tried multiple times and have not been able to get the right answer. "If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives is 4.5% of the total...
  45. T

    Is Your Friend's Radiation Exposure in Guarapari Safe Compared to UK Standards?

    Homework Statement A friend tells you that she is planning to change her life by moving from the UK to the Brazilian resort of Guarapari, where she intends to make and sell food on the beach for the tourists for 8 hours a day, every day. Whilst pleased for her adventurous plan, you are a little...
  46. alijan kk

    How to solve a percentage word problem for profit?

    Homework Statement A person lost 10% when he sold goods at Rs 153 for how much should he sell them to gain 20% . Homework EquationsThe Attempt at a Solution 0.10(153)= 15.3 153+15.3= 168.3 ( the price of product for no profit) 0.2(168.3)=33.6 (168.3+33.6)= 201.9 rupees is the 20% gain ...
  47. alijan kk

    Solve Ratio Word Problem: A & B in 30 & 40 Days

    Homework Statement A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ? Homework EquationsThe Attempt at a Solution I just imagined walls and paiting work and try to assign them and i found that it tooks 55 days working...
  48. I

    Student Loan Payment Calculation and Effective Interest Rate Analysis

    Homework Statement You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% APR (monthly). You are considering making an extra payment of $100 today (i.e., you will pay an extra $100 that you are not required to...
  49. M

    An equation for an algebra word problem

    Homework Statement Suppose that b is 20% more than a, c is 25% more than b, and d is k% less than c. Find k such that a=d Homework Equations a=d; b=1.2a; c=1.25b=1.5aThe Attempt at a Solution 1. a=##\frac{c}{15 }##=d=##\frac{100c-k}{100}## 2. By multiplication of extremes and means we get...
  50. A

    Energy and Momentum [Spring (word problem)]

    Homework Statement [/B] Please check the attachments as to view the questions. Homework Equations Ek= 1/2 mv^2 EPSpring= 1/2 kx^2The Attempt at a Solution A) EPSpring= 1/2 kx^2 1/2 (100)(0.11) ^2 =0.605 JB) Is ok I understand it. C) EKO=EKFEPSpring(Initial) + EK(Initial) =...