See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
Stars indicate particularly interesting answers or
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Selected answers to common questions:
- 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
- Sales and Taxes [03/11/2001]
I bought $27.97 worth of food. The food tax is 5.5%. I'm trying to find
the tax I have to pay, and the total amount that I pay.
- Same Day Off? [12/08/2002]
One person has every ninth day off and started on Sunday, and
another person has every sixth day off and started on Monday. When
will they both be off on the same day?
- Savings on Gasoline [05/22/2001]
Your old car averaged 22 mpg and you new car should average 37 mpg.
Suppose you drive 12,500 miles per year and the cost of gas averages
$1.85 per gallon. How much will you save on gasoline each year?
- Sergeant Marco's Maintenance Check [3/11/1995]
Corporal Jones takes 12 hours to complete a planned maintenance check on
an anti-submarine helicopter. Jones had been working on a helicopter for
4 hours when sergeant Marco arrived to help him finish the job. They
complete the check in 2 hours. How long would it have taken Sergeant
Marco to complete the job alone?
- Setting Up Algebraic Word Problems [08/04/2003]
If each photocopy of a manuscript costs 4 cents per page, what is the
cost, in cents, to reproduce x copies of an x-page manuscript?
- Setting Up Equations [11/26/1997]
An airplane travels eight times as fast as a car. The difference in their
speeds is 420 km/h. How fast is each vehicle travelling?
- Setting Up Proportions and Unit Conversions [7/25/1996]
If you can run 100 meters in 10 seconds, how long, in days, hours, and
minutes, does it take you to run 12,800,000 meters?
- Setting Up the Equation for a Word Problem [2/1/1996]
How many apples do I have if I get 22 from my mom and twice as many from
my dad and then have to give half to my sister and have to throw away 8
of them because they are bad?
- Several Ways to Solve a Rate-Time-Distance Problem [02/14/2006]
A bus leaves point A travelling at a speed of 10 mph. 22 minutes
later a car leaves point A travelling in the same direction as the bus
at 40 mph. At what distance will the car catch the bus, and how much
time will have elapsed since the car left point A?