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Word Problems

Browse Middle School Word Problems
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Mixture problems.

One Chicken, One Day [04/19/2002]
If a chicken and a half lays an egg and a half in a day and a half, how many eggs can one chicken lay in one day?

On or Off? [05/26/2001]
How can I determine whether an automatic sprinkler system is on or off at 3:30 A.M., based on timed observations by the night watchman?

Orange and Grape Sodas [08/24/2002]
Douglas bought a total of 50 cans of orange and grape sodas. He bought 12 more cans of grape than orange. How many of each did he buy?

Organizing the Information in an Algebraic Word Problem [09/05/2007]
A word problem involving baseball teams and numbers of wins gives a good example of how to use each of the many clues given in the problem to work toward writing an equation and solving the problem.

Palindromic Number Word Problem [9/4/1995]
A palindromic number reads backwards and forwards the same way, e.g. 1221 and 696. What is the number of years until the next palindromic calendar year?

Passing Cyclists [08/31/2003]
Two cyclists ride on the same road in opposite directions, passing each other twice...

Passing Mr. Jones [09/30/2002]
Mr. Jones lives 50 miles away from you. You both leave home at 5:00 and drive toward each other. Mr. Jones drives at 35 mph and you drive at 40 mph. At what time will you pass Mr. Jones on the road?

Passing Ships [05/12/1999]
Every day a ship leaves San Francisco for Tokyo... How many Tokyo ships will each San Francisco ship meet?

Passing the Ball [09/27/1997]
How long would it take to pass a basketball from one person to another 2833 miles from San Francisco to Washington, DC?

Pennies and Remainders [01/13/2003]
Arnie has between 300 and 400 pennies in his collection. When he divides them into groups of 4, 5, or 9, there is always one penny left over. How many pennies does Arnie's collection contain?

The Pharaoh's Will [05/16/2000]
As he lay dying, the Pharaoh proclaimed: "I bequeath 1/3 of my estate to my oldest child; 1/4 of my estate to the next oldest child; and to each succeeding child, except the youngest, the next unit fraction of my estate; and to the youngest the remainder."

Pipe Needed for Natural Gas Line [09/03/1997]
Two houses are 130 metres apart at distances of 55 and 105 metres...

Plane Flying with a Tailwind [9/8/1996]
A jet is flying 2400 miles from Hawaii to San Francisco. In still air, it flies at 600 mph. There is a 40 mph tailwind...

Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.

Possible Combinations from Cards Drawn at the Same Time? [04/02/1998]
If two of four numbered cards are drawn at the same time, how many possible combinations could be made?

Presidential Logic [10/28/2002]
A history test has three questions on Presidents of the United States...

Price before Discount [6/3/1996]
A calculator's price is discounted 20 percent. After adding 7 percent tax...

Price of House, Commission [8/29/1996]
If a real estate agent recieves 6 percent of the selling price of each house she sells, then what should be the sale price of a house if a seller wants to keep $61,000?

Price of Pencils [10/07/2002]
Each year for the last 7 years the price of pencils has increased, and the new price is the sum of the prices for the two previous years. Last year a pencil cost 60 cents. How much does a pencil cost today? How much did a pencil cost 7 years ago?

Price Plus 1/2 Price [12/05/2001]
A puzzle book costs $5.00 plus one-half of its price. How much does the puzzle book cost?

Probate Puzzle [12/15/2003]
A will specifies that every son should receive three times as much as a daughter and every daughter should get two times as much as their mother. What is the mother's share?

Problem about Rain [09/20/2000]
During a recent span of time, 11 days had some rain... How many days had no rain at all?

Problem Solving and Mental Process [10/03/2002]
Two numbers add up to 19. The difference between the two numbers is 3. What are the numbers?

Problem-solving Strategies [11/01/2001]
Are there suggestions you can make that might be helpful?

Problem-Solving: Systems of Equations [4/27/1996]
Figuring the cost of printing business cards.

Problem Sums [5/31/1996]
John has 36 more sweets than May, while Peter has 20 fewer...

Profit and Percent Waste [6/13/1996]
A fruit-seller buys 240 apples for $60, but some are bad. Calculate the percent thrown away.

Profit From Selling Chairs [9/5/1996]
A man buys 3 chairs for $50. He sells them for $24 each. How many chairs must he sell to make a profit of $1320?

Profit on a Sale [11/25/1994]
An investor bought 12 acres of land for $70,000. She later subdivided the land into 22 lots that she sold for $4500 apiece. What was her profit on the sale?

Profit or loss? [6/17/1996]
Mr Li paid $120 for a basket of 40 durians. He found that four of them were bad and threw them away. What was his profit or loss?

Proportions of Men to Women [4/18/1996]
In a certain village 2/3 of the men are married to 3/5 of the women. What proportion of the population as a whole is married?

Prorating the Rent [09/19/2002]
If my rent is $127 and I moved in on the 11th of this month, what will my prorated amount be for September?

A Quadratic Word Problem [07/27/1999]
If the robbery rate per 1000 persons is increased by two and then decreased by 6, the product of the rate increased by 2 and the rate decreased by 6 is 180. What is the rate?

Questions Answered Correctly [06/11/2003]
There are 30 multiple-choice questions in a contest. Five marks are awarded for each correct answer, and three marks are deducted for each incorrect answer. No marks are awarded for questions left unanswered. If a student scores 78 marks, what is the greatest possible number of questions answered correctly?

Rates of Paddling [04/25/2000]
I can travel 12 miles downstream in six hours less than it takes me to travel the same distance upstream... How fast is this river's current?

Rates of Work Combined, and Staggered [08/24/2010]
How quickly would one person complete a task that he finished with the help of a second worker? A student writes in with a standard algorithm for combining rates of work, but this problem features a variation that stumps him. Doctor Ian suggests reframing the units of the job to make the problem more approachable.

Ratio and Proportion [7/4/1996]
Six men can complete a piece of work in one day... 44 men can build a tower in 5 days...

Ratio and Proportion: Beaches and Hawks [10/26/1998]
On a map, the scale states that 3 inches represent 125 miles. Two beaches are 5.2 inches apart. How far apart are they in miles?

Ratio and Proportion: Jobs [7/7/1996]
30 men can complete a job in 12 days at 8 hours/day. How many hours/ day will it take to complete the job in 10 days with 24 men?

Ratio of Anti-Freeze to Water [02/05/2003]
A barrel is filled with 45 gallons of anti-freeze. 9 gallons are removed and the barrel is refilled with water. 9 gallons of the mixture are removed and again, the barrel is refilled with water. What is the final ratio of anti-freeze to water in the barrel?

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