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:
- Tartaglia's Riddle, Redux [09/22/2012]
"If half of 4 were 3 ..." Doctor Peterson explains the intent behind this puzzling riddle,
which reminds him of a classic stumper.
- Tea and Cakes [11/13/2002]
A cafe sold tea at 30 cents a cup and cakes at 50 cents each. Everyone
in a group had the same number of cups of tea and the same number of
cakes. The bill came to $13.30. How many cups of tea did each person
- Tea Blend: Price of Inferior Tea [6/24/1996]
6 kg of inferior quality tea are mixed with 3 kg of high quality tea.
What is the price of the inferior tea?
- Test Average Word Problem [02/20/2004]
In a certain class there are more than 20 and fewer than 40 students.
On a recent test the average passing mark was 75. The average
failing mark was 48 and the class average was 66. The teacher then
raised every grade 5 points. As a result the average passing mark
became 77.5 and the average failing mark became 45. If 65 is the
established minimum for passing, how many students had their grades
changed from failing to passing?
- Three Freighters [10/11/1997]
Three freighters leave St. John's, Newfoundland, for Montreal, Quebec at
the same time...
- Three Pieces of Wire [01/07/1998]
A florist cuts a wire into 3 pieces. The 1st piece is 20% of the 2nd; the
3rd piece is 110% of the 2nd. The wire is 23 cm long; how long is each
- To Multiply or Divide? That Is the Question. [09/02/2003]
In a story problem, how do you know whether to multiply or divide?
- Total Test Questions [09/21/1997]
On her biology test, Cathy answered 5/6 of the questions correctly...
- Town Population [05/02/1997]
The population of town A is 4800 more than town B. If 3100 people move
from town B to town A, the population in town A will be 11 times that of
town B. Find the original total population of the two towns.
- Train and Tunnel [07/18/2001]
A freight train 800 metres long is travelling at a constant speed of 18km
per hour... when does the rear of the train emerge from the tunnel?
- Train B Overtakes Train A [01/17/2002]
Train A leaves the station traveling at 30 miles per hour. Two hours
later train B leaves the same station travelling in the same direction at
40 miles per hour. How long does it take for train B to catch up to train
- A Train Breaks Down [06/30/2001]
A train breaks down an hour after starting its journey. After repairs, it
can only continue at half its original speed and arrives at its
destination two hours late...
- Train Overtaking Another Train [10/19/1996]
Two trains leave a station, one an hour after the other...
- Train Speed, Wind, and Smoke [7/2/1996]
An electric train is climbing a hill at 45 kph...
- Trains, Speed, and Tunnels [09/10/1998]
A 500m train passes through a 2000m tunnel and 60 seconds elapse between
the last car entering and the engine exiting...
- Translating Word Sentences to Math Sentences [03/10/2004]
"Six more than three times x is four times two less than x" was
translated in our textbook to 6 + 3x = 4(x - 2). Some of my students
felt it should be 6 + 3x = x - (4*2). Is there a true rule or law of
mathematics or some definite tradition as to the interpretation of
- Traveling Buses [06/01/1997]
A southbound bus left Fort Walton Beach at 9:00 A.M. Two hours later a
northbound bus left the same station... find the rates of the buses.
- Traveling Trains and Nonlinear Systems [07/16/1998]
A train leaves town A and travels 540 miles at a uniform speed, followed
an hour later by another train.... What were the speeds of the trains?
- Travelling Trains [11/6/1994]
I've always wondered about those two trains that left the East coast and
the West coast. The question asked when they would meet or where they
would meet if both left at the same time and were traveling at 60 to 70
mph. I know that isn't the exact question, but that has always stuck in
the back of my mind. Care to try and figure out some kind of reply, even
though the question is sort of hazy?
- T-Shirts and Shorts [8/24/1996]
In the evening, a sporting goods store sells twice as many as many T-
shirts as shorts...
- Turning Word Problems into Equations [04/15/2002]
I don't like turning word problems into equations because it is too
confusing. Is there a technique that might help me out?
- Turning Word Problems to Equations [03/08/2001]
How do you turn English sentences into math equations?
- Two Cars on Crete [08/15/1997]
Find the speed of the car from Phaistos.
- Two Coins Problem [11/22/2006]
I have two U.S. coins that when added together total fifty-five cents,
but one is not a nickel. What two coins do I have?
- Two-equation Rate Problem [09/26/1999]
Ellie drives 264 km in the same time that Carol takes to drive 198 km.
Ellie's speed is 17 km/hr greater than Carol's. What is each woman's
- Two Numbers in 5:3 Ratio [12/07/2002]
Two numbers have a ratio of 5:3. The larger number is 36 more than
half the difference of the two numbers. What are the two numbers?
There are two pairs of numbers that will make this a true statement.
You need to find both of them.
- Two People are Faster than One [4/17/1996]
It takes Mary 100 hours longer than Ken to drink a case of beer. If it
takes 2 hours to drink the case together, how long would it take Mary to
drink the case alone?
- Two Pipes and a Drain [01/07/1998]
A swimming pool has 2 inlet pipes. One fills the pool in 4 hrs., the
other in 6 hrs...
- Two Planes and Not Enough Information [08/10/2004]
Two planes leave Chicago, one traveling due east and the other due
west. The first travels 100 miles per hour faster than the second.
How long will it be until they are 2000 miles apart?
- Two Quantities, Two Relations [04/04/2000]
Find two consecutive numbers whose squares, when subtracted, equal 43.
- Two Steps Forward, One Step Back [10/14/2003]
A salmon swims 30 feet upstream in 5 seconds, then rests for 2
seconds. If she moves 10 feet downstream during each rest, how long
does it take her to swim 1010 feet?
- Unitary Method Problem [02/01/1999]
How many runts are there in 6 cartons if each carton has 8 packages -
each of which has 3 boxes (each of which has 170 runts)?
- Units and Cylinder Volume [02/06/2003]
Find the volume and surface area of a cylindical storage tank with a
radius of 15 feet and a height of 30 feet.
- Use One Weighing [02/06/2002]
There are 90 genuine coins and 10 fake coins in 10 stacks with 10 coins
in each stack... Using only one weighing, determine which stack contains
the fake coins.
- Using Guess and Check to Start an Algebra Problem [02/15/2008]
Laura is three times as old as Maria was when Laura was as old as
Maria is now. In two years Laura will be twice as old as Maria was two
years ago. Find their present ages. Dr. Ian shows that by first making
a guess and checking it you can then easily write the algebraic
equations needed to solve the problem.
- Using Improper Fractions in a Word Problem [12/6/1995]
Mr. Smith owns 1/4 of the stock of a business. Mrs. Smith owns 5/6 as
much as Mr. Smith. How much do they not own of the stock?
- Using Tables to Tame a Problem [09/19/2003]
Racing bikes are either silver or blue. Every silver bike is
a racing model. 1/2 of the blue bikes are racing models. 1/3 of the
bikes are racing models. There are 40 blue bikes and 30 silver
bikes. How many bicycles are neither blue nor silver?
- Using Units and Variables to Make Sense of Word Problems [05/24/2004]
I am having a hard time changing a word problem into a formula in
order to get the results. For example: Apples cost $1.50 per pound
and pears cost $2.30 per pound. A total of 8 pounds of apples and
pears were bought, and the price was $14.00. How many pounds of pears
- Using Variables to Solve Word Problems [05/10/1998]
Susan puts only dimes and quarters in her coin bank ...
- The Value of a Word [08/25/1998]
Think of a word that equals one dollar. The key is: a=.01, b=.02, c=.03,