# 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...

23. ### 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. ### 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. ### 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...
45. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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) =...