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Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
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Selected answers to common questions:
- Find the Angles [9/11/1996]
The first angle of a triangle is eight degrees more than two times the
third angle. The second angle is two degrees less than three times the
third angle. Find all three angles.
- Find the Heavier Coin of 12 in 3 Weighings [11/17/1996]
If there are twelve coins in a bag, one of which is either lighter or
heavier than the others, find the fake coin in exactly 3 weighings AND
determine if it is lighter or heavier than the others.
- Find the Numbers [08/28/2003]
One number is 61 more than a second number. The sum of the two
numbers is 127. Find the numbers.
- Five Bags of Nuts [04/17/2002]
Given 100 nuts in five paper bags, in the first and second bags there
are altogether fifty-two nuts; in the second and third there are
forty-three; in the third and fourth, thirty-four; in the fourth and
fifth, thirty. How many nuts are there in each bag?
- Flipping for Profit [01/19/2014]
A young entrepreneur struggles to reverse-engineer the mark-up price that
guarantees his take-home profit. Starting with his own steps as a framework, Doctor
Peterson introduces variables and applies algebra to model the scenario more
- Football Scoring [11/24/2002]
What was the number of points scored by the red team? What is the
smallest number of scoring plays that the red team could have made
to get its point total?
- For a Given Number, Solve the Expression... [6/28/1996]
For a given number m, m greater than or equal to 1 , solve: The square
root of m + x plus the square root of m - x divided by the square root of
- Formulas and Missing Quantities [10/09/2004]
Variations on the question "Could you drink enough water in a lifetime to empty a pool?" lead to a discussion of using formulas to find missing quantities.
- Four Methods of Solving Classic Chicken and Egg Problems [02/24/2009]
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to
kill 100 rats in 50 minutes? A look at four different solution methods
for this sort of problem.
- Fractions and School Enrollments [02/26/2003]
The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School
is exactly the enrollment of the Language School. The sum of 1/5, 1/6,
1/7, and 1/8 of the enrollment of the Business School is exactly that
of the Design School. What are the enrollments of these three schools,
assuming no school has more than 1000 pupils?
- Fractions: Sheets of Paper Left [08/07/1997]
An office got a new copier and was given 800 sheets of paper. On the
first day they used 1/3 of the paper...
- From Representing Two Bags of Marbles, a Way to Solve All Kinds of Problems [04/03/2011]
A student struggles with an algebra word problem. Doctor Ian breaks it down into
manageable chunks, stepping through how to represent the question's relationships
algebraically and then check his interpretation for reasonableness.
- From Word Problems to Equations [01/28/1999]
If the sides of a square are lengthened by 3m, the area becomes 81m
squared. Find the length of a side of the original square.
- Garden Areas [8/14/1996]
Was the second garden larger or smaller?
- Getting the Job Done [12/17/1996]
Two typists share a job and each does half of the work. The second typist
begins working one hour after the first...
- Giraffe Height [9/9/1996]
A newborn giraffe 6 feet tall is 1/3 the height of an adult giraffe. How
much taller is the adult?
- Girls and Coins [01/29/2001]
Five girls stopped for a soda on the way home from school. The girls were
amazed to find that each of them had exactly six coins...
- Golf Balls [04/13/1997]
Angie bought some golf balls for $14. If each ball had cost $0.25 less...
- Guess and Check - How Many Coins? [10/03/2002]
Jeremy has seven fewer coins than Hanna. If together they have 83
coins, how many coins does Hanna have?
- Guess and Check Tables, Algebra [10/12/2002]
Find the mass of Hector's math, science, and Spanish textbooks.
- Handcar and Freight Train [12/6/1994]
A handcar sets out from Chicago to Detroit at an average speed of 10mph.
Four hours later a freight train starts a run from Detroit to Chicago at
an average speed of 20 mph. Assuming the rail distance between the two
cities is 400 miles, which will be closer to Chicago when they meet?
- Helicopters Over a Traffic Jam [09/23/1998]
A helicopter flies over a traffic jam at a speed of 180 km/h...
- Hines Parkway Problem [2/4/1995]
What is the average speed of cars on Hines Parkway given the following
- Hot Air Balloons [12/25/1996]
A hot air balloon covered 2100 miles in 7 days. If it covered 50 miles
more each day than the day before, how many miles did it cover each day?
- How Do You Figure Out the Equations for Word Problems? [04/09/2006]
I can solve equations fine, but whenever I try a word problem, I can't
figure out how to come up with the equation I need to solve. How do
you turn a word problem into the right equation?
- How Far Did the Plane Fly? [01/23/2003]
A plane flew 440km/h to its destination. It then flew 500km/h back. If
the whole trip took 9 hours, how far did the plane fly?
- How Fast Did Dan Drive? [8/24/1996]
It takes Kay 20 minutes to drive to work at 45 mph. Two minutes after she
left home this morning, her husband Dan started out...
- How Heavy is the Brick? [11/15/1997]
If a brick weighs a kilogram plus half a brick, how heavy is the brick?
- How Long is Duke the Dog? [09/04/2001]
Duke the dog's head is 6 inches long, his tail is as long as his head
plus half the length of his body, and his body is as long as the head and
the tail combined.
- How Long is the Train? [05/21/1999]
Two trains are traveling in opposite directions along parallel tracks,
train A at 72kph and train B at 54kph...
- How Many Apples? [09/19/2002]
How many apples did John get from his boss?
- How Many are in the Group? [10/17/1996]
Everyone in the group had been to at least one of the parks...
- How Many Barbies [08/11/1999]
How many different Barbies can I make if I can choose from 4 skin colors,
3 eye colors, 4 hairstyles, and 6 hair colors?
- How Many Boys Are in the Seventh Grade? [05/20/1999]
In a seventh grade of 360 students, 80 percent can swim...
- How Many Coins Did Each Originally Have? [10/22/2001]
Natalie has some nickels, Dirk has some dimes, and Quincy has some
quarters. Dirk has five more dimes than Quincy has quarters... How many
coins did each originally have?
- How Many Days in the Month? [01/22/2004]
There were eleven days of rain one month in Boston. Of the remaining
days, two-fifths were sunny, one-fourth were cloudy, and it snowed the
other seven days. How many days were in the month?
- How Many Different Combinations of Shares Could She Buy? [03/05/1998]
Mrs. Ridero has $240 that she wants to invest in three companies traded
on the stock market ...
- How Many Freshmen Originally Tried Out? [01/15/2003]
Some freshmen were trying out for the school track team... The 10 who
remained became the track team.
- How Many Men, Women, and Children at the Circus? [10/18/2000]
A circus performance is witnessed by 120 people who have paid $120. The
men paid $5, the women $2, and the children $.10 each. How many of each
went to the circus? A solution without algebra.
- How Many Mice, Cats, and Dogs? [01/13/2003]
You must spend $100 to buy 100 pets, choosing at least one of each
pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00
each, and dogs @ $15.00 each. How many mice, cats, and dogs must you