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

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  6. C

    Using a Problem Solving Technique for a simple word problem

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  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

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  11. N

    Trigonometry - Cricket related word problem

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  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

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  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

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  16. A

    MHB Word problem for winning percentage

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  17. J

    MHB Real Estate math word problem help

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  18. K

    MHB Algebra word problem solve for x

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  19. L

    MHB Introductory Algebra Percentage Word Problem

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  20. karush

    MHB 2.2.294 Euler's method word problem

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  21. S

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  22. R

    MHB High school simple algebra word problem

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  23. M

    MHB Joint CDF of a word problem

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  24. T

    Python Finding the day from a given date

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  25. F

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

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  26. M

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

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  27. T

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  28. T

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  29. J

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  30. alijan kk

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  31. Charge

    Adding Vectors to Find Velocity

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  32. opus

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    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

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  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

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  37. opus

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  38. G

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

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  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

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  41. M

    Shoot a basketball with a minimum speed at some angle

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  42. phantom lancer

    Physics Word Problem: Arrow and moving target collision

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  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

    Radation Dosage word problem

    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

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  50. A

    Energy and Momentum [Spring (word problem)]

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