See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
- 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
- Price before Discount [6/3/1996]
A calculator's price is discounted 20 percent. After adding 7 percent
- 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
- 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?
- Ratio of Rates and Work [06/06/1998]
Given the rates of 5 semi-skilled and 4 skilled workers, can you find how
long it takes 1 semi-skilled and 2 skilled workers to do a job?
- Ratios and Mixtures [05/10/2001]
Sue needs to mix up a potion for her client... in what ratio must Sue mix
the honey and turpentine?
- Ratio Set-Up Problem [09/02/2003]
Concrete can be made by mixing cement, sand, and gravel in the ratio
3:6:8. How much gravel is needed to make 850 m^3 of cement?
- Reba's Physics Problems [12/09/2001]
Reba's dad said he'd pay her a quarter for each correct answer and fine
her a dime for each incorrect answer. She received $3.80 after doing 25
problems. How many problems did she answer correctly?
- Reciprocal Rate [11/28/2001]
An automobile gets 20 miles per gallon of fuel. Compute the reciprocal
rate giving units of measurement.
- Road Under Construction [9/8/1996]
On a 6-hour, 295 mile trip, Adam traveled at 50 mph except where there
was construction, when he went 40 mph. How many miles of road were under
- Rounding Off an Answer to Fit the Situation [09/12/2004]
Are there times when you might round an answer up or down based on the
situation in the problem and not the standard rounding rules?
- Rowing Upstream and Down [5/9/1996]
Karen can row a boat 10 kilometers per hour in still water...
- Running Problem (Time and Distance) [8/31/1996]
If Lucy runs 3 mph and Jan runs 7 mph, when will Jan catch up with Lucy
if she gives Lucy a head start?
- The Sailor's Reward Problem and Prime Numbers [12/11/2004]
Does the answer to the classic Sailor's Reward problem have to be a