The Math Forum

Ask Dr. Math

Middle School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

This page:
  word problems checkmark

  Dr. Math

See also the
Dr. Math FAQ:
  classic problems
  word problems


About Math

   factoring expressions
   graphing equations

   factoring numbers


     conic sections/
   3D and higher



Number Sense
   factoring numbers
   negative numbers
   prime numbers
   square roots

Word Problems

Browse Middle School Word Problems
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Mixture problems.

Distance, Rate and Time [6/3/1995]
Ian travelled by train at 80km/h and then by car at 90 km/h. It took him 3 hours to travel the total distance of 265km. How far did he travel during each phase of his journey, and how long did each phase take?

Distance, Rate, and Time Problems [3/22/1995]
Liza and Tamar leave the same camp and run in opposite directions. Liza runs 2m/s and Tamar runs 3m/s. How far apart are they after 1 hour?

Distance/Time [12/8/1995]
Bernice is cycling around a track at 15 mph. Betty starts at the same time, but only goes 12 mph. How many minutes after they start will Bernice pass Betty if the track is 1/2 mile long?

Dividing 17 Rings [10/22/1996]
How was the inheritance divided?

Does Unit Price Always Give the Best Buy? [12/30/2007]
Which is the best buy, 13 videos for $25 or 11 videos for $20? It seems like there are a couple ways to analyze the question.

Dog Food Mixture [10/23/2002]
A grocer wishes to mix 6 pounds of Chippy dog food worth $3 per pound with Hippy dog food, worth $4 per pound. How much of the Hippy dog food should be mixed if the dog food mixture is to sell for $3.20?

Doubling Bacteria [09/17/1997]
How many bacteria are in the colony?

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 different numbers.

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?

Exceedingly Fractious Equation [09/05/2016]
A non-native English speaker struggles to parse the clues in a riddle. By focusing on one overlooked key word, Doctor Fenton starts to unravel the unknown.

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 alone?

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 integers.

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?

Page: [<prev]  1  2  3  4  5  6  7  8  9 10 11 12 13 [next>]

Search the Dr. Math Library:

Search: entire archive just Middle School Word Problems

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994- The Math Forum at NCTM. All rights reserved.