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:
- How Many Seats? [01/15/2003]
There are 40 rows in an auditorium. Each has two more seats than the
previous row. There are 1960 seats in all. How many seats are in the
first row of the auditorium?
- How Many Steps on the Escalator? [7/1/1996]
A famous mathematician who is always in a hurry walks up an up-going
escalator at the rate of one step per second. Twenty steps bring him to
- How Many Stickers...? [8/25/1996]
James has twice as many stickers as John, who has twice as many stickers
- How Many Trains Meet? [09/17/2001]
Every hour, on the hour, a train leaves Tallahassee for Jacksonville,
while another train leaves Jacksonville for Tallahassee. The trip between
the two cities takes exactly two hours. How many trains going in the
opposite direction will a Tallahassee train to Jacksonville meet?
- How Many Valentines? [02/10/2003]
If everyone in your class gave a Valentine to everyone else in your
class, how many valentines would be exchanged?
- How Much did the Tree Grow? [11/07/2001]
A white pine was 16 m tall in 1962. It was 20 m tall in 1965. It is now
34 m tall. How much has it grown since 1962?
- How Much Does the Youngest Boy Get? [05/25/2000]
Five brothers, each born in a different year, share a gift of $100...
- How Much Money Entering the First Store? [09/26/2002]
Timothy spent all of his money at five stores. At each store, he spent
$1 more than half of the amount he had when entering the store. How
much money did he have when he entered the first store?
- How Much Popcorn did Paul Sell? [01/28/2002]
Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22
selling popcorn and $2.62 selling beer, how many boxes of popcorn were
- How Much to Add? [01/16/1998]
Tonya must add to a mixture enough of a substance to make the whole weigh
2.5 grams - how much should she add?
- How Much Water Evaporated? [06/19/2003]
A substance is 99% water. Some water evaporates, leaving a substance
that is 98% water. How much of the water evaporated?
- How Old Are John and Julia? [05/17/2001]
Julia is as old as John will be when Julia is twice as old as John was
when Julia's age was half the sum of their present ages. John is as old
as Julia was when John was half the age he will be 10 years from now. How
old are John and Julia?
- How Old at $4,000? [10/15/2002]
Aunt Isabella gives each niece and nephew $10 on his or her first
birthday, and on each birthday thereafter the children get $20.00 more
than on the birthday before. How old will a child be when he or she
receives a total of $4,000.00?
- How Old Did This Man Live to Be? [02/23/1998]
A word problem involving fractions.
- How Old in 1900? [11/09/2002]
In 1930, a correspondent proposed the following question: A man's age
at death was one twenty-ninth of the year of his birth. How old was
the man in 1900?
- How Old is Korinth? [09/09/1997]
Korinth is twice as old as Marin was when Korinth was as old as Marin is
now. Marin is 18.
- How to Interpret "Increase" in Word Problems [10/19/2004]
How do I increase 3.7 by 1/10?
- How Wide is the River? [7/2/1996]
Two ferryboats ply back and forth across a river with constant but
- The Importance of Defining Variables Clearly in Algebra [11/01/2007]
A sample of dimes and quarters totals $18.00. If there are 111 coins
in all, how many are there of each coin?
- Inconsistent System of Equations? Look Closer! [11/17/2004]
When Alexis, Chelsea, and Kammi had lunch together, Alexis spent $1.60
for two small hamburgers, a drink and one order of fries. Chelsea's
two orders of fries, two drinks and one small burger cost $1.40
altogether. How much does Kammi owe for a small burger, one order
of fries and one drink?
- Increase in Chicken Consumption [8/29/1996]
In 1984 the average American ate 55.7 lbs. of chicken. This was 2.8 lbs.
more than the average in 1982. What was the percent of increase in
- Increasing the Average [02/25/2001]
Five members of a basketball team are weighed and an average weight is
recalculated after each weighing. If the average increases 2 pounds each
time, how much heavier is the last player than the first?
- Inequalities: Add or Subtract? [10/21/2001]
Sometimes, when doing inequalities problems, I have to add or subtract
one from the answer I have calculated. I don't understand when to add,
subtract, or do nothing at all.
- Integer problem [11/30/1994]
Find the largest possible 2 integers such that the larger integer is more
than 3 less than 3 times the smaller one.
- Interpreting "Less" and "Less Than" in Word Problems [10/18/2004]
Find all numbers such that 9 less than the product of the number and
-4 is less than 7.
- Introduction to Linear and Exponential Growth [11/04/2003]
A population of beetles increases from 5 to 15 after one month. How
many beetles will there be after 4 months if the population is
increasing linearly? What if it's increasing exponentially?
- Is Henry Guilty? (Geometry Puzzle) [6/10/1996]
In Hughmoar County, residents shall be allowed to build a straight road
between two homes as long as the new road is not perpendicular to any
existing county road...
- Isolating Groceries from Total Expenses, and Problems from Paragraphs [09/03/2011]
Given functions in a word problem, an adult student doesn't know how to begin
subtracting one from the other. Before clarifying her use of variables, Doctor Peterson
suggests reading through the problem strategically, to distill it down to just algebraic
- Jack Climbing the Beanstalk [6/29/1996]
Jack climbed up the beanstalk at a uniform rate. At 2 P.M. he was one-
sixth the way up and at 4 P.M. he was three fourths the way up...
- Jeep [04/07/1997]
A jeep can carry 200 liters of gasoline and can drive 2.5 km/l. You want
to travel 1000 km...
- Jim and Joe Drive toward Each Other [12/05/2001]
Jim and Joe leave their homes at the same time and drive toward each
other... how far apart were they when they started?
- John's Losing His Marbles [8/26/1996]
How many marbles did John have before he lost 42 green ones?
- Jupiter and Saturn [09/10/2001]
Jupiter revolves around the Sun about once every 12 earth years; Saturn
about once every 30 earth years. In 1982, Jupiter and Saturn appeared
very close to each other. When will they appear together again?
- Key Words to Suggest What Operation to Use [12/08/2005]
Are there words or phrases like 'in all' that help suggest what
operation to use to solve a word problem?
- Knights of the Round Table [07/01/1998]
If x knights are sitting at a round table, and every other one is
removed, who is the last one left sitting at the table?
- Laying Eggs Better by Half [12/05/2001]
If a hen and a half lays an egg and a half in a day and a half, how many
and a half that lay better by half will lay half a score and a half in a
week and a half?
- Leaky Ship [08/15/1997]
How many men are needed to pump a ship dry in 2 hours?
- Lemonade Proportions [04/02/1998]
If lemonade is made with a ratio of 3 cups water to 2 cups lemon juice,
how many cups of lemon juice are in 10 gallons of lemonade?
- Longfellow's Bees [08/01/2002]
One-fifth of some bees fly to the rosebush, one-third fly to the
apple tree, and three times the difference fly to the acorn tree. One
bee is left flying around. How many bees are there altogether?
- Lower Percents: Capacity and Consumption [02/03/2013]
A consumer wants to know how the battery life of her new mobile phone compares to
that of her old one. Doctor Peterson introduces the notion of judiciously selecting the