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Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
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Selected answers to common questions:
- 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
- Machine Pizza [08/15/1997]
A machine for processing pizzas puts salami on every 18th pizza...
- Making the Grade [04/13/2001]
After three tests, Amanda's average score is 88. What grade does she need
on her next test to score a four-test average of 90?
- Making up a Division Word Problem [11/13/2001]
Write a problem that could be solved by using the division sentence
1489/28=n; then write a pair of compatible numbers and estimate the
- Man Crossing a Bridge [09/27/2001]
A man is jogging across a bridge at 8 mph. When he is 3/8 of the way
- Mangoes and Oranges [8/21/1996]
Miss Tay paid $14 for 5 mangoes and 8 oranges. If each mango costs $1.50
more than each orange, what is the cost of each mango?
- Man on a Railroad Bridge [09/20/1998]
A man is on a bridge and hears a train behind him. He has just enough
time to run to either end to prevent being hit. How fast can he run?
- Marble Collection Fraction Problem [9/9/1996]
3/4 of Tim's marble collection is the same size as 3/5 of Danny's
- Maths Problem Involving Lateral Thinking [5/24/1996]
Binh and Duong start running in opposite directions on a circular track.
...How many times will they meet?
- Maximizing Revenues [07/29/2002]
For every increase of $1 in ticket price, 200 fewer people will attend
each game. What ticket price will maximize revenues?
- Measuring the Length of a Moving Train [08/12/2003]
I was driving in the opposite direction from a moving train that had
many cars behind the locomotive. It took me approximately 2-3 minutes
from the time my car 'met' the front of the train until it passed me
going the opposite direction. My speed was about 40 miles an hour. Is
it possible to estimate the length of this moving train without
actually measuring when it is not moving?
- The Missing Dollar [03/29/1997]
Three men went to a restaurant for dinner and spent $30, but the cashier
gave the waiter back $5. The waiter kept $2...
- The Missing Dollar Gets Dressed Up [12/27/2014]
Two adults dispute how to solve a seemingly innocuous word problem. Doctor Ian
reveals the red herring in this arithmetic puzzle related to the classic accounting riddle
of a motel bellboy and a missing dollar.
- Mixing Copper-Silver Alloys [06/09/1999]
How much of each type of two copper-silver alloys is needed to produce
1.2 kg of alloy containing 62% pure silver?
- Mixing Peanuts and Cashews [11/19/1999]
Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How
many pounds of cashews should be mixed with 12 pounds of peanuts to
obtain a mixture that sells for $4.20 per pound?
- Mixture Problem [11/11/1997]
How much pure antifreeze should be added to 3 gallons of a 30 percent
antifreeze solution to get 65 percent antifreeze?
- Monetary Conversions [01/27/2001]
Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2
mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya
and for papaya to mango?
- Monkeys Dividing the Coconut Pile [07/28/1998]
A monkey divides a pile of coconuts into three, tosses the extra one, and
takes his share...
- Monkeys Eating Peanuts [6/22/1996]
Four monkeys eat four bags of peanuts in three minutes...
- Mopey & Zegro [11/3/1994]
Boggs can carry two hartsels or three choloes. Mopey can carry three
hartsels or five choloes. Zegro can carry 7 hartsels or nine choloes...
- Mother's Age in Terms of Daughter's [06/27/2001]
The sum of the ages of a father, a mother, and a daughter is 73. When the
father is twice as old as the daughter, the sum of their two ages will be
- Mowing Half a Lawn [03/31/2002]
Chris and Lee are each responsible for mowing half of their 50-foot by
90-foot rectangular back yard...
- Mr. Brown's Walk [09/09/1997]
One day Mr. Brown took the 4:00 p.m. train, arrived at the station one
hour early, and started walking home... How long did Mr. Brown walk?
- Mr. Thomas' Salary [9/6/1996]
Mr. Thomas spent 1/12 of his salary to buy a watch and 3/11 of the
remaining to pay for a new television set... what was his salary?
- Ms. Krump's Age [10/05/1999]
This year I'm 3 times as old as my little sister; 6 years ago I was 5
times as old as she was. How old am I?
- Multiple Percentages [1/26/1996]
You have a pair of jeans. Every time they are washed, they lose 5 percent
of their color...
- Multiplying Mice [07/23/1997]
Baby mice can breed when they are 6 weeks old and the babies are born
after 3 weeks. If each mother mouse has only one litter and all the
litters have 8 babies, half males and half females, how many mice will
you have 18 weeks from today?
- Nine Chickens, Ten Days [02/26/2002]
If a chicken and a half lays an egg and a half in a day and a half
then, how many eggs will nine chickens lay in ten days?
- Nonsense Solutions to Word Problems [04/28/2003]
Bill, Simon, and John are brothers. Bill is as many years younger than
one brother as he is older than the other. Simon is 7 years younger
than twice the age of John. John is 5 years older than half the age
of one of his brothers. I keep getting -3 for Simon's age. What am I
- Number * Sum of Remaining Four Numbers [04/03/2003]
Find 5 numbers such that when each number is multiplied by the sum of
the remaining 4 numbers, the following values will result: 152, 245,
297, 320, 360.
- One Billion Seconds [09/27/1998]
If I was born on 01/02/84, on what day, month, and year will I have been
alive for a billion seconds?
- 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?