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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If the investment earns interest at the rate of 16% compounded quarterly, then each cash flow is

Suppose a person invests $20,000 in a business venture that guarantees the same cash flow at the end of every quarter for four years. If the investment earns interest at the rate of 16% compounded ...
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Count the number of dimes?

You are given a bag with 100 coins.  The bag only has pennies, dimes and half-dollars.  The bag has at least one of each coin.  The total value of the coins in the bag is worth $5,  How many dimes are ...
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How many crates will there be?

I’m working on the following riddle: UPS can fit 8 large packages or 10 small packages in a crate for shipping. In one shipment, they can send a total of 96 packages. If there are more large packages ...
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How many pieces of lumber do I need to make a box?

I've started building raised gardens boxes of custom sizes. For a given box of width $x$ and length $y$, how many boards of lumber of length $l$ do I need to build this box? Assume (for now) the ...
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How long to catch up to a stream started $1$ hour ago at $1.5$x speed?

I opened a stream that started an hour ago. Not wanting to miss anything, I started from the beginning and set it to 1.5x speed. How long will it take for me to catch up? I know that it will take 40 ...
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3answers
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Pierre runs a game at a fair, where each player is guaranteed to win $10 - Die rolling question

Pierre runs a game at a fair, where each player is guaranteed to win $10. Players pay a certain amount each time they roll an unbiased die, and must keep rolling until a ‘6’ occurs. When a ‘6’ ...
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1answer
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Linear algebra word problem with hourly wages

The painter, the plumber and the electrician set up the joint venture and agreed to work within it for ten hours each week according to the following schedule. For example, the first column ...
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Flower probability word problem [closed]

A garden plant can produce pink, white or blue flowers. The probability of the plant having pink flowers is 0.5. Blue and white flowers are equally likely. What is the probability of a plant having ...
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Math Trigonometry [closed]

Bert, Ernie, and Elmo each have their owns tents and are camping at Grand Bend. From Bert’s location, Bert estimates that Ernie’s tent 630 m from his, on a true bearing of 100°. Bert estimates that ...
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Stuck on Algebra › Solving by multiplying [closed]

I'm practicing maths and got stuck at certain point. Isn't the answer 48? If I write 48, it says "try again". Correct me if I'm wrong. please see image here
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Word problem on differentiation

I am studying for my exams and do not know if I tackled correctly this word problem. Would appreciate any help. Thank you Question a): Write down an expression for the area $A$ in terms of $w$ and $...
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How to find p for which the profit will be a maximum in this context?

A producer of computer graphics software finds that selling price p of its software is related to the number of x copies of its software sold annually by the demand equation, x = 10000 -200p , while ...
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Bayesian Problem: What is the Expected number of mattresses that the Princess slept on?

It's been a while since I've done some Bayesian problems but I'm looking for some help with the following: "Each night, a princess is equally likely to sleep on anything from six to twelve ...
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In the Library of Count Dracula

Am thinking about this question from the book Analysis $1$ by Herbert Amann and Joachim Escher: In the library of Count Dracula no two books contain exactly the same number of words. The number of ...
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1answer
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Please help me figure this out How many options are their?

Kylie is having a BBQ for the senior class of 2020! She will be serving hamburgers, hotdogs, and brats. There will be coleslaw, potato salad, fruit, and pasta salad for sides. She has cake, cookies, ...
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Sum of all integers from $1$ to $20$ except one is a multiple of $20$

Sam was adding the integers from $1$ to $20$. In his rush, he skipped one of the numbers and forgot to add it. His final sum was a multiple of $20$. What number did he forget to add? My idea was to ...
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1answer
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Princess Sarah work problem

Princess Sarah and Becky are peeling potatoes. Given the same number $P$ of potatoes, Princess Sarah can finish peeling them alone $2$ hours and $36$ minutes before Becky can, alone. If Princess Sarah ...
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1answer
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Finding the 4th algebraic equation for word problem?

For the word problem below, there are 4 variables to solve for, but I can only identify 3 equations given the data. Through trial and error, you can easily figure out the answer, but I am wondering if ...
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Clock Math: Finding the current time when the minute hand and hour hand are opposite to each other

Problem It is now between 10:00 and 11:00 Six minutes from now, the minute hand of a watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now? ...
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1answer
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Ratio & Proportion word problem

I had a doubt regarding a question. My answer is coming as 10 even though I've tried using another method and according to my book, the answer is as 7.5. Can anybody help if possible? (Also, hope we ...
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1answer
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The present ages of Shakti and Selene are in the ratio 10:3. After 3 years, the ratio becomes 23:9. Find the difference in their ages after 17 years.

I just wanted to know if there is any shortcut to solve this kind of questions orally, The present ages of Shakti and Selene are in the ratio 10:3. After 3 years, the ratio becomes 23:9. Find the ...
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1answer
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An elementary probability theory problem

I have just started learning probability theory and came across this problem, In each packet of Corn Flakes may be found a plastic bust of one of the last five Vice-Chancellors of Cambridge ...
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Using laws of sine and cosine solve the problem

Julius lives on Wolfhorn Island, which is 55 miles directly west of Gypsum Island, where Donuttella lives. Julius sees a buoy at heading N 37° E. Donuttella sees the same buoy at N 49° W. What is the ...
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3 Toast Problem From “Thinking Mathematically”: Solution Check

I am working through "Thinking Mathematically" by Mason, Burton and Stacey. One of the questions goes as follows: Three slices of bread are to be toasted under a grill. The grill can hold two slices ...
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compound interest deposits and withdrawals

I am trying to solve the following problem: My bank pays ρ% interest at the end of each year. I start with nothing in my account. Then for m years I deposit £a in my account at the beginning of each ...
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Not able to understand the statement in the given word problem.

Q- A computer solved several problems in succession. The time it took to solve each successive problem was the same no of times smaller than the time it took to solve the preceding problem. How many ...
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1answer
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Which is the correct answer for reaching the airport gate the fastest?

I'm taking the 'Introduction to mathematical thinking - Keith Devlin' and in the Problem Set Solutions, there's a question: You've arrived late at an airport. You're rushing to catch your plane. ...
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7answers
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$12$ men can finish a job in $16$ days. $5$ men work at the start; and after 8 days, 3 men were added. How many days needed to finish the whole job?

Twelve men can finish a job in 16 days. 5 men were working at the start and after 8 days, 3 men were added. How many days will it take to finish the whole job? Solution: So, the job will take $12 \...
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1answer
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Two airplanes depart at the same time

Two airplanes depart at the same time from Paris to London. One flies with a velocity of 350 km/h and the other flies with v=280 km/h. After 2 hours, the first airplane decreases its velocity with 230 ...
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1answer
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How can we prove this for n=5, 13 and any values?

A man has to paint n consecutive mile posts and wants to do this as inefficiently as possible - So that he walks as far as possible from the first post he paints to the last post he paints. He can ...
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1answer
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calculating margin offset in order to stack playing cards to fit inside box

So, I have x amount of cards and a container width that is variable. I am trying to calculate how much minus margin i have to apply to each card in order to make them all fit inside the container. I ...
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Calculate percentage of a path segment

This problem should be quite simple but I am having a hard time getting to the solution... Imagine that I have the following path: ...
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2answers
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How do I set up the following Differential Equation?

so in the following word problem, it seems that I am supposed to solve a differential equation in order to find the function f. However, with the way it is worded, I'm having a tough time actually ...
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Word problem that I need help explaining! Can someone break this down for me?

There are $32$ students in Mrs. Vicky’s class. Some of the students took one pencil each from the box with pencils on the teachers desk. Then a third of the remaining students took $3$ pencils each, ...
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Processor Word Problem

It takes 12 processor 5 min to calculate 6 solutions. If 40 processor are in two groups, where grou 1 has 4 more processors than the 2nd group, how long will it take the 2nd group to calculate 27 ...
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Setting up a differential model

I'm confused on how I set up a differential model for this problem. Any help would be appreciated. A hot cup of coffee is placed in a room with a wack temperature control. The coffee at T(0) is 160 ...
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How to find the number of pills which someone has consumed given a time range?

The problem is as follows: Marina went to the doctor and he has advised her to take vitamins. As doctor's orders she has to take one tablet of Vitamin C every 6 hours. From vitamin D she has to ...
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3answers
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How can I find the a certain birthdate of two people when one information given depends on the other?

The problem is as follows: Mike was born on $\textrm{October 1st, 2012,}$ and Jack on $\textrm{December 1st, 2013}$. Find the date when the triple the age of Jack is the double of Mike's age. The ...
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word problem with natural numbers?

Jenny writes the natural numbers from 1 to 1001 in a row. Can the signs ”+” and ”-” be placed between the numbers in such a way that the value of the resulting expression is 100? If yes, show ...
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Object slides from a surface's frictionless part to a rough part. How long does it take to stop?

A rectangular prism of length $L$ is sliding on a flat surface with speed $v_0$, without friction. It slides onto a rough section of the surface where the coefficient of kinetic friction is $\mu$. ...
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Please help with this Ratio question [closed]

Pritam, Sarah and Emily share some money in the ratios 3:6:4 Sarah gets $15 more than Emily. Work out the amount of money that Pritam gets?
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1answer
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How can I find the number of bell tollings when the time elapsed has powers?

The problem is as follows: A clocktower has a mechanism which strikes a bell and this indicates the number of hours which is exactly the same as the number of bell tollings. To indicate $2^n\,a....
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1answer
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How to formulate this maximisation problem?

Question "A company offers the following schedule of charges: $30 per thousand for orders of 50,000 or less, with the charge decreased by 37.5 cents for each thousand above 50,000. Find the order ...
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Application of Ordinary differential equations

A large lake is to be formed by damming a river which holds initially 100million gallons of water. The water got contaminated with a pesticide of concentration of 35ppm (parts per million). The river ...
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1answer
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Need help with word problem

I am trying to solve this problem. Can someone please help me with the proper solution. My answer is "$2$ hours," but I want a step by step solution I can teach to my kid. Problem: A tiger eats a ...
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4answers
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Translate this logical statement into natural language.

I am trying to translate this logical statement into English: $\forall x(x<10 \implies \forall y(y < x \implies y < 9))$. Note that the statement is true when the universe of discourse is $\...
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2answers
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Andi and Brandi cycle around a field, with velocities: 8 km/h and 4 km/h. What is the perimeter of the field?

$Andi$ and $Brandi$ cycle around a field, starts at same position and at same time with same direction. $Andi$'s and $Brandi$'s velocity are $8$ km/h and $4$ km/h. After one lap, $Andi$ took a rest ...
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2answers
108 views

geometry question from kangaroo math contest

drawing A rectangle has sides of length 6cm and 11cm. One long side is selected. The bisectors of the angles at either end of that side are drawn. These bisectors divide the other long side ...
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1answer
67 views

Roller coaster quiz (to be solved with the determinant and affine plane)

The problem is as follows: Four dwarfs had taken a friend, let's call him Joe, to the fair. After some time they finally found the roller coaster. Everyone was already sitting in their own wagon - ...

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