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Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
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Selected answers to common questions:
- 100 Percent of Daily Allowance of Iron [09/30/2001]
A common foodstuff is found to contain .00125% iron. The serving size is
87.0 grams. If the recommended daily allowance is 18mg of iron, how many
servings would a person have to eat to get 100% of the daily allowance of
- Acid Concentration, Heating Bill [7/6/1996]
1) A pharmacist has 8 liters of a 15 percent solution of acid. How much
distilled water must she add.... 2) By installing a $120 thermostat, a
family hopes to cut its annual heating bill...
- Age and Money [12/13/1994]
Frank is eight years older than his sister. In three years he will be
twice as old as she is. How old are they now? (and other similar
- Backward Through the Steps [5/20/1996]
Can you show strategies for solving this baseball card word problem?
- Blending Seed [09/27/1998]
How much of $0.65/lb seed does a dealer need to combine with 200 lbs of
$0.45/lb seed to make a $0.55/lb blend?
- Calculating Income vs. Sales [3/26/1996]
A factory owner knows that some of her expenses are going to occur
regardless of how many items she makes. These are fixed costs and total
$3000 per week...
- Conversions [3/17/1995]
Nancy ran a distance of 3.8km in 55 min. Calculate her speed in
kilometers per hour and metres per second.
- Cost of Cleaning a Building [07/03/2003]
If I clean a 3200 square foot building five nights per week for a sum
of $575.00 per month, what is the cost per square foot?
- Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003]
All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?
- Diesel or Gasoline Engine? [10/16/1996]
You can buy a car with a diesel engine for $427.65 more than the same car
with a gasoline engine...
- Dimensional Analysis [10/06/2001]
Mr. R wants to give all of his chemistry students enough chocolate to
make them goofy for the rest of the day. It's a known fact that it takes
47 chocolate chips to make a student goofy...
- Employee Pay Schedule [07/12/2003]
For a particular job, Moe should get 40% of the gross pay, Larry
should get 30%, and Curly should get 30%, assuming they all work the
same number of hours. But how should the money be divided if they
work different numbers of hours?
- Equations from Word Problems, and Units [05/19/2003]
In 2 1/4 hours the temperature dropped 13 1/9 degrees. How many
degrees did the temperature drop per hour? How do I convert this
from words into an equation?
- Factoring Problems [8/14/1996]
What is the width of an uniform border surrounding a rectangle?
- Farmer Crossing a River [09/24/2001]
A farmer is taking his prize lettuce, lion, llama, and pet leviathan (a
unique creature that eats llamas and lions unless a lettuce is present)
- Finding One Coin of 12 in 3 Steps [8/6/1996]
Given a pile of twelve coins of equal size with one of a different
weight, in three weighings find the unequal coin...
- Finding Sally's Hourly Wage [11/7/1994]
Sally works at a grocery store. In one week she earned $390 for working
47 hours, of which 7 hours were overtime.The next week she earned $416
for working 50 hours, of which 8 hours were overtime. What is Sally's
- Finding the Ages of the Farmer's Daughters [12/21/1995]
A man has three daughters. The product of their ages is 72, the sum of
their ages is his house number, and the oldest loves chocolate. What are
the daughters' ages?
- Gold Medal-Winning Times, and Their Corresponding Distances: Applied Math in the Real World of Sports [08/30/2016]
A coach from Team USA wants to show his Olympians the distance that separates
them from a gold-medal finish. Using results from a race that they lost by less than
half a second, Doctor Wilko applies the distance-rate-time formula to illustrate the
margin of victory.
- Guessing Your Way to Algebra: On Rates, Remainders, Relationships, and Restraint [09/08/2013]
John spent 2/5 of his money on exercise books, and 1/3 of the remainder on three
ballpoint pens, which cost eight times as much per. Doctor Ian steps through this word
problem by using numeric guesses as placeholders before declaring variables
— and making a key insight.
- How Many Boxes? A Diagram [03/20/2003]
There were juice boxes in a cooler. Jared took 1/6 of them. Sara took
1/4 of what was left. Now there are 15 boxes. How many boxes were
there to start with?
- How Many Chickens and Ducks? [8/16/1996]
A man bought 20 chickens and ducks, with a $2 discount per chicken and 50
cent discount per duck...
- How Many Stools? How Many Tables? [12/13/2002]
In their spare time, the Buffalo Bills operations staff members build
3-legged stools and 4-legged tables. Last month they used 72 legs to
build 3 more stools than tables.
- How much is the dagger worth? [10/12/1996]
A sword and dagger are together worth 300 copper pieces. The sword is
worth 200 copper pieces more than the dagger. How much is the dagger
- How Much Money is Left? [5/1/1995]
A lady has a certain number of dollar bills in her purse. She has no
other money. She spends half the money on a hat and gives $1 to a beggar
outside the store. She spends half the remaining dollars for lunch and
tips the waiter $2. She then spends half the remaining dollars for a
book, and just before she goes home she spends $3 on a hot fudge sundae.
She now has $1 left. How many dollars did she begin with?
- How Old are Ben and Kris? [10/17/1999]
Five years ago Ben was 2/3 as old as Kris. Ten years from now he will be
5/6 as old as Kris. How old are they now?
- How Old is Chris Now? [12/26/2001]
Pat is twice as old as Chris was when Pat was as old as Chris is now. If
Pat is 24 now, how old is Chris now?
- How to Turn Word Problems into Algebra Equations [6/6/1996]
Where do you put the letters and numbers when setting up algebra
equations from word problems?
- Least Common Multiple Word Problem [12/10/1996]
Each of three businesses receives different sized cartons of glasses. If
all three receive the same number of glasses and none of them receive
more than a thousand glasses, how many glasses and cartons are in each
- Least Number of Marbles [2/20/1995]
After a successful game of marbles with three friends, Joe said, "If only
I had one more marble, ...." What is the least number of marbles Joe
could have had?
- Markups and Discounts [02/12/2002]
What is the correct way to mark up or discount a product?
- Math Age Word Problem [03/20/2001]
Bob is as old as John will be when Bob is twice as old as John was when
Bob's age was half the sum of their present ages...
- Math Logic [6/5/1996]
Sally, Ron, Jim, and Meghan are President, VP, Treasurer, and Captain of
the cheerleading squad, but not necessarily in that order. Who is what?
- Mixing Alcohol, Cable TV Pricing [8/2/1996]
What amounts of 9 percent and 12 percent alcohol do you mix to get
300,000 gallons of 10 percent alcohol? For each 5-cent increase in the
monthly subscription price, 4 people will decide not to subscribe to
- Mixing Milk and Butterfat [09/04/2001]
Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How
much of each is needed to obtain 60 gallons of milk that has 3%
- Number of Quarters [9/11/1996]
Tony has eleven more nickels than quarters. How many quarters does he
have if the total value of his coins is $2.65?
- Number Puzzle Solved with and without Algebra [12/10/2001]
I am a number. Add 25 to me. Divide the sum by 2. You end with 75. What
number am I?
- Pencil Costs, Dividing Property [6/25/1996]
1) Drawing pencils cost 8 cents each and colored pencils cost 11 cents
each. Two dozen assorted pencils cost $2.16. How many colored pencils are
there? 2) A man died, leaving 23 cows to his three children; the eldest
child should have 1/2 of the cows...
- Radius of a Pizza [8/27/1996]
If a pizza has an area of 30 inches, what is its radius?
- Rate of Travel [05/15/2003]
A passenger on a train traveling at 135km/h walks toward the back of
the train at a rate of 7km/h. What is the passenger's rate of travel
with respect to the ground?