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:
- Doubling Opposite Integers [04/19/1998]
On a number line, a certain integer is 24 units away from the double of
its opposite. What is the integer?
- Egg Doubling Problem; UK & US: Naming Large Numbers [5/6/1996]
The sixtieth time you double them, you have a lot of eggs! How many
rectangles would they fill if each egg is one unit?
- Elimination Method in Real Life [03/30/2003]
If 3 tall candles and 5 small candles cost $7.30, and 2 tall candles
and 2 small candles cost $3.40, how much does 1 tall candle cost? How
much does 1 small candle cost?
- Equal Sum, Product, Quotient of Two Numbers [10/13/2002]
I need to know the sum, product, and quotient, all equal, of two
- Equations - Al and his father [12/6/1994]
Write an equation: Al's father is 45 years old. This is 15 more than
twice Al's age. How old is Al?
- Equivalent Expressions / Equivalent Equations [07/27/1997]
Could you please explain the difference between equivalent expressions
and equivalent equations?
- Escaping the Tiger [07/10/2003]
A man stands in the center of a circle. On the circumference is a
tiger that can only move around the circle. The tiger can run four
times as fast as the man. How can the man escape the circle without
being eaten by the tiger?
- Estate Distribution [05/10/1999]
Does 1/10 of the estate go to the church before or after taxes?
- Estimating Seating Capacity [05/10/2000]
How can I estimate how many chairs can be placed in the seating area of a
convention center meeting room that is 80 feet across at the front, 120
feet across at the rear, and 150 feet from front to back?
- Evaporation [12/08/2003]
A substance is 99% water. Some water eveporates, leaving a substance
that is 98% water. How much of the water evaporated?
- Factoring vs. an Equation [10/01/2002]
The product of two consecutive odd numbers is 255. Find the numbers.
- Farmer, Goat, Wolf, and Cabbage Cross a River [03/13/1998]
Fewest number of trips a farmer can make to get a goat, wolf, and cabbage
across a river.
- Feeding Chickens - Arithmetical Progression [7/6/1996]
A farmer has 3000 hens. Each week he sells 20... what is the total cost
of feeding the hens...?
- Fencing Two Back Yards [01/27/2001]
Sarah and Jane want to put a fence around their two rectangular back
yards, with a single fence separating the yards... If they share the cost
of the fence equally, how much will each of them pay?
- Fibonacci and Possible Tilings [09/24/2003]
You are going to pave a 15 ft by 2 ft walkway with 1 ft by 2 ft paving
stones. How does the Fibonacci sequence relate to the number of
possible ways that the walkway can be paved?
- Fifty-two Cards, Three Piles ... One Coincidence? [02/20/2013]
Why does the "count on" card trick work? Doctor Peterson revisits a card-counting
curiosity with greater clarity.
- Filling a Pool [07/28/1997]
It takes 2 hours to fill a pool with one hose, and 5 hours with another.
How long does it take to fill the pool with both hoses?
- Filling a Tank [08/01/1997]
How long will it take two pipes together to fill a tank?
- Filling a Tank [12/19/2002]
A tank is filled by two pipes. The smaller pipe alone will take 24
minutes longer than the larger pipe and 32 minutes longer than when
booth pipes are used. How long will each pipe take to fill the tank
- Filling a Tub [6/11/1996]
If one faucet fills a tub at a certain rate, and another faucet at
another rate; how fast will the tub fill if both are open?
- Filling Perfume Bottles [03/11/1997]
Three girls have a 24-ounce bottle of perfume which they want to divide
equally among them. They have 3 empty bottles. How can they divide the
perfume so that each girl has eight ounces in a bottle?
- Find Depth of Water in a Tank [08/02/2003]
A rectangular tank measures 4m long, 2m wide and 4.8m high. Initially
it is half full of water. Find the depth of water in the tank after
4000 litres of water have been added to it.
- Finding a Formula for Mixtures [11/10/2003]
Alfredo needs to make 250 ml of a 27% alcohol solution, using a 15%
solution and a 40% solution. How much of each should he use?
- Finding Age in an Algebra Word Problem [12/8/1995]
Doris is as much older than Joris as Joris is older than Boris. Five
years ago Doris' age was double what the age difference between her and
Joris will be 15 years from now. How old is Boris?
- Finding Ages: Tot and Teen [12/01/2002]
Tot is now half as old as Teenager was when Tot was a third as old as
Teenager is now.
- Finding an Equation for a Fish Word Problem [12/8/1995]
A boy breeds goldfish as a hobby. He decides to sell all his fish. He
does this in five steps...
- Finding a Number [4/13/1996]
My ones digit is twice my tens digit. One of my factors is 3. What am I?
- Finding Integers Given LCM and GCD [11/05/2002]
The least common multiple of two positive integers is 144, and the
greatest common divisor is 2. Neither integer is 2. Find both
- Finding Numbers Using Their Product [3/24/1996]
The product of two consecutive integers is 240. What are the integers?
- Finding the Cost of Pets in a Pet Shop [2/26/1996]
In a large pet store, the sign above the fish tank says, "Buy sixteen
fish and eight cats for the price of seven dogs"...
- Finding the Cost of Washers in Relation to Bolts [12/8/1995]
Jacob Handyman has been told that 50 identical bolts and 20 identical
nuts cost $9.10, whereas 30 nuts and...
- Finding the Number of Fishbowls Sold [3/15/1996]
Trivia took some fishbowls to a flea market. In the first hour she sold
one-third of them and a third more; in the second hour, she sold half of
them and a half more; in the third hour she sold one-third and a third of
one more; the next hour she sold half and half of one more; finally, she
sold the last two. How many fishbowls did Trivia sell?
- Finding the Weight of an Egg [2/9/1996]
If an egg weighs 20 grams and half an egg, what does an egg and a half
- Finding Two Numbers with Known Product and Difference [08/06/2008]
Two numbers have a product of 6800 and a difference of 5. Find the
numbers. How can I solve this without using algebra?
- Finding Units [4/14/1996]
The two digits in the numerator of a fraction are reversed in its
denominator. If 1 is subtracted from both the numerator and the
- 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?
- 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?